# How do I find the sum of a geometric series from 2 to infinity of -3/ (4^n) ?

94,438 questions
1. ## Calc II

Use the comparison or limit comparison test to decide if the following series converge. Series from n=1 to infinity of (4-sin n) / ((n^2)+1) and the series from n=1 to infinity of (4-sin n) / ((2^n) +1). For each series which converges, give an

asked by Lauren on November 7, 2012
2. ## calculus

find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if

asked by sarah on March 21, 2008
3. ## math(need 2nd opinion)

1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 A)15 B)15/2 C)-15 D)1/15 I chose A 2)Find the sum of the infinite geometric series. Sigma sign with infinity symbol above and n=1 below. To the right 20(-1/4)n-1 A)25 B)80/3 C16 D)does not exist

asked by Jon on December 12, 2007
4. ## math

1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 A)15 B)15/2 C)-15 D)1/15 I chose A 2)Find the sum of the infinite geometric series. Sigma sign with infinity symbol above and n=1 below. To the right 20(-1/4)n-1 A)25 B)80/3 C16 D)does not exist

asked by Jon on December 12, 2007
5. ## calculus

Another problem: determine whether the series is convergent if so find sum it is the sum from k=1 to infinity of ((-1)^k)/(3^(k+1)) i found this series to be geometric where a=-1/9 and r=1/3 my answer was converges to 1/6

asked by sarah on February 21, 2008
6. ## calculus

determine whether the series is convergent if so find sum it is the sum from k=1 to infinity of ((-1)^k)/(3^(k+1)) i found this series to be geometric where a=-1/9 and r=1/3 my answer was converges to 1/6

asked by sarah on February 21, 2008
7. ## Arithmetic

A geometric series has a positive common ratio of r. The series has a sum to infinity of 9 and the sum of the first two terms is 5. Find the first four terms of the series.

asked by samuel on November 25, 2017
8. ## calculus

How do I find the sum of a geometric series from 2 to infinity of -3/ (4^n) ?

asked by tom on March 11, 2019
9. ## Calculus

Determine convergence or divergence for the following series. State the tests used and justify your answers. Sum (infinity, n=1) 1/(1+e^-n) Sum (infinity, n=1) (2*4*6...2n)/n! Sum (infinity, n=0) (n-6)/n Sum (infinity, n=0) (n-6)/n! Sum (infinity, n=0)

10. ## plz sequence sir steve reiny bob damon i need u

The three real,distint and non-zero numbers a,b,c are such that a,b,c are in arithmetic progression and a,c,b are in geometric progression. Find the numerical value of the common ratio of the geometric progression.. Hence,find an expression in terms of a

asked by pooo on January 6, 2017
11. ## CALC II

Determine the convergence of the following series using the nth-partial sum or geometric series formula. The sum of n=1 to inifitiy 1/(9n^2+3n-2) How do I start? I'm guessing I should factor out the denominator but whats after that? It is close to a

asked by Ace on June 18, 2007
12. ## Arithmetic

Find a geometric series which has a third term of 7/4 and a sum to infinity of 14.

asked by Piwo on April 10, 2012
13. ## Maths

Find the sum to infinity of the geometric series n=1 ,3/10n =3/10+3/1000+....................

asked by Zanele on May 9, 2013
14. ## Pre-Calculus

Q.Determine the sum of each infinite geometric series. t_1= 8 r = -2^1/2 ---------------------------------------- A.This is a divergent series because the absolute value of r is greater than 1. ---------------------------------------- Q. The first term of

asked by Lucina on February 17, 2015
15. ## Algebra

Use the geometric sequence of numbers 1, 1/3, 1/9, 1/27… to find the following: Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.

asked by Gina on October 29, 2006
16. ## Calculus III

Which of the following series are geometric series? Find the sum if they are 1. Infinity (Summation sign) n = 1 1/6n^2 2. Infinity (Summation sign) n = 1 (0.6)^n-1

asked by kile on December 10, 2007
17. ## algebra

1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16 d.does not exist answer=c

asked by Marissa on August 24, 2007
18. ## algebra(check)

1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16 d.does not exist answer=c

asked by Marissa on August 24, 2007
19. ## algebra

1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16 d.does not exist answer=c

asked by Marissa on August 23, 2007
20. ## algebra

1)Find a1 in a geometric series for which Sn=300,r=-3,and n=4 a.15 b.15/2 c.-15 d.1/15 answer=a 2)Find the sum of the infinite geometric series n=1 at the bottom of the sigma notation 20(-1/4)n-1 on the right side a.25 b.80/3 c.16 d.does not exist answer=c

asked by Marissa on August 26, 2007
21. ## Calculus

Which of the following statements is true for the series the summation from n=0 to infinity of (-1)^n and 5/4^n? a) The series diverges because it is geometric with r = 5/4 and a = –1. b) The series converges to 4 because it is geometric with r = -1/4

asked by Alice on May 13, 2019
22. ## Math

Does the following infinite geometric series diverge or converge? Explain. 1/5 + 1/25 + 1/125 + 1/625 A) It diverges; it has a sum. B) It converges; it has a sum. C) It diverges; it does not have a sum. D) It converges; it does not have a sum. I am pretty

asked by M, S, E, on May 4, 2017
23. ## Mathematics

State whether this infinite series converges or diverges? 1+(t) + (t^3)+...... t=[(5x+6)/(3x-2)] My thoughts on the question: The sum of 'n' terms in a geometric progression is a[r^n - 1]/(r-1)--(let's calk this 1), where r>1 and when r

asked by Shenaya on June 8, 2017
24. ## math

(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also

asked by Edwin on September 23, 2009
25. ## math

(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also

asked by Edwin on September 23, 2009
26. ## CALC 2

a. Consider the following limit as a fact: lim n-> infinity ((n!)^1/n)/n = 1/e Use this limit to study the convergence of this series using the root test. Sum of infinity and n=1 of ((3^n)n!)/n^n b. Use the ratio or the root test to determine the

asked by Bae on April 6, 2014
27. ## algebra

Okay, I was taught that if a geometric series is infinite and it diverges then it has no limit and no sum. Looking back in my notes, I found an example of finding the value for a divergent series? Is this possible? The sum of an infinite geometric

asked by Jane E. on May 31, 2007
28. ## Taylor seires

f(x) =ln (1-x) a) Compute f'(x), f''(x), f'''(x). Spot the pattern and give an expression for f ^(n) (x) [the n-th derivative of f(x)] b) Compute the MacLaurin series of f(x) (i.e. the Taylor series of f(x) around x=0) c) Compute the radius of convergence

asked by Jill on November 26, 2006
29. ## calculus

determine whether the series is convergent if so find sum: the sum of x=3 to infinity of (k+1)^2/((x-1)(x-2)) is it infinity meaning it diverges?

asked by sarah on February 21, 2008
30. ## math C2 sequences and series

The eight,fourth and second terms of an arithmetic progression form the first three terms of a geometric series. The arithmetic progression has first term A and common difference d, and the geometric progression has first term G and common ratio r. a)Given

asked by Stephan on January 2, 2017
31. ## Math *URGENT

Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646? 3. Determine the geometric mean of 8

asked by Aliza on December 20, 2012

Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following: b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.

asked by Vianna on November 4, 2006
33. ## Calc

Does 1/ln(x+1) converge or diverge? I've tried the nth term test, limit comparison test, and integral test. All I get is inconclusive. The other tests I have (geometric series, p-series, telescoping series, alternating series, and root tests) don't apply.

asked by Mischa on March 22, 2007
34. ## Algebra 2

I need steps on how to complete this please i am so confused and lost. :( Consider the infinite geometric series x e n=1 -4(1/3) n-1. In this image, the lower limit of the summation notation is "n=1". a. Write the first four terms of the series. b. Does

asked by Sammy on March 10, 2015
35. ## Calculus 2

Use the formula for the sum of a geometric series to ﬁnd the sum or state that the series diverges. (4/9)^n starting at n=-4

asked by RaShawnya on March 28, 2018
36. ## Algebra 2

Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first four terms of the sequence? a{1} = first term of series                ∞    Infinite Sum = ∑  a{1} •

asked by Ke\$ha on March 31, 2016
37. ## arithmetic

1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four

asked by kartik hans on May 24, 2014
38. ## arithmetic

1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four

asked by kartik hans on May 23, 2014
39. ## calculus

Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(

asked by Megan on April 22, 2010
40. ## Calculus

Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(

asked by Megan on April 21, 2010
41. ## calculus

Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(

asked by Megan on April 22, 2010
42. ## College Calculus (Binomial Series)

Expand f(x) = (x+x^2)/((1-x)^3) as a power series and use it to find the sum of series (SUM from n=1 to infinity) (n^2)/(2^n) PLEASE HELP.

asked by Andrew on April 8, 2008
43. ## algebra

Can someone please help me with this problem? Thanks! Evaluate the infinite geometric series: 8+4+2+1+... I thought you needed to know the number of terms to evaluate, but how do you know them if it is infinite? The limit of Sn = 1 + r + r^2 + r^3 + r^4 +

asked by Mercy on May 30, 2007
44. ## math studies

An arithmetic series has a first term of -4 and a common difference of 1. A geometric series has a first term of 8 and a common ratio of 0.5. After how many terms does the sum of the arithmetic series exceed the sum of the geometric series?

asked by ll on September 28, 2008
45. ## Geometric Series

Evaluate the geometric Series or state that it diverges lower bound k= 1 upper bound = infinity E (sum symbol) E 5(-1/6)^(5k) I know it converges but im not sure to what

asked by Kate on May 7, 2015
46. ## Calculus

Given that the series the summation from n=1 to infinity of [(-1)^(n+1)/√n is convergent, find a value of n for which the nth partial sum is guaranteed to approximate the sum of the series to two decimal places. a) 39,999 b) 3,999 c) 399 d) 39

asked by Alice on May 13, 2019
47. ## Calc 2

Use the ratio or the root test to determine the convergence of the series: Sum of infinity and n=1 of arctan(e^-n), Sum of infinity and k=1 of sqroot(3^k)/(2^k)

asked by Bae on April 6, 2014
48. ## calculus

Determine whether the series is convergent o divergent and say what test you used to solve it. (d) sum n=1 to infinity (5n)^(3n) / (5^n + 3)^n (e) sum k=1 to infinity 5 / sqr(2k - 1)

asked by Paul on September 20, 2012
49. ## Math

Consider the following series: 1,2,3,4,5,10,20,40....which starts as an arithmetic series? ...but after the first five terms becomes a geometric series. Prove that any positive integer can be written as a sum of distinct numbers from the series. I know how

asked by MO on May 17, 2016
50. ## calculus

i have to determine whether the series is convergent, and if, find the sum the series is from k=1 to infinity of 2/((k+1)(k+3)) I got 5/6 as my answer and didn't know if it was right...

asked by sarah on February 21, 2008
51. ## Calculus

For what values of p>0 does the series Riemann Sum [n=1 to infinity] 1/ [n(ln n) (ln(ln n))^p] converge and for what values does it diverge? You need to let the summation start at n = 3 to avoid the singularity at n = 1 (although you can formally take

asked by Janice on November 13, 2006
52. ## calculus

determine whether the series converges of diverges the sum from k=2 to infinity of (the square root of (ln(k)))/k I said that because you can't integrate the series (goes to infinity) it diverges is this true?

asked by sarah on February 26, 2008

I need help answering these questions 1. State the Common Ratio of the following Geometric sequence 3/4 , 3/10 , 3/25 , 6/125 2. In the Arithmetic Sequence below, X = ___ 100 , ___ , _X_ , 64 3. For the Geometric Sequence below, X = ___ _X_ , 48 , ___ ,

asked by Temour on March 23, 2009
54. ## trig

for the geometric series shown, state whether the series in convergent. If the Series is convergent give its sum 9+6.3 +4.41 +... a tutor helped me earlier but how is the sum 0.7

asked by jerson on November 10, 2008
55. ## math

determine the difference between the sum of the infinite geometric series 18-6+2-2/3...and the sum of the first 6 terms of the series (round to 3 decimal places) first i did S=18/ (1+1/3)= 13 1/2 Sn= 18(1+(1/3)^6) _____________ 1 + 1/3 = 13 14/27 13 1/2 -

asked by s on November 17, 2008
56. ## calculus

determine whether the series converges of diverges the sum from k=2 to infinity of (the square root of (ln(k)))/k I said that because you can't integrate the series (goes to infinity) it diverges

asked by sarah on February 26, 2008
57. ## Math.

The first term of a geometric series is 4 and the sum of the first three terms of the series is 64. Find the sum of the first eight terms of the series.

asked by Tom on January 8, 2014
58. ## math help!!

the first term in a geometric series is 4 and the sum of the first three terms of the series is 64. find the sum of the first eight terms of the series.

asked by nikki on December 16, 2014
59. ## math

the last two tems in a geometric series are 1080 and 6480 and the sum ofthe series is 7775 what is the first term in the series

asked by Heather on December 18, 2011
60. ## calculus

how do you find the sum of a series? for example: the series from n=0 to infinity of (-1)^n/n!??? thanks

asked by sarah on March 20, 2008
61. ## algebra

consider the infinite geometric series n=1 -4(1/3)^n-1 . i need help with writing the first four terms of the series and finding the sum if it has a sum.

asked by on March 18, 2019
62. ## ALG 2

Find the sum of the geometric series given.....(if their is no sum...state no sum) 3+9+27...

asked by Embraced on January 24, 2012
63. ## calc.

find the sum of the series of (-2)^n/3^n+1. This is an alternating series... what if we rewrite it as an= (1/3)* (-2/3)^(n) Divide any nth term by the n-1 term and see if you get a ratio term r. This might be a geometric series.

asked by kelly on April 17, 2007
64. ## math

Find the sum of the infinite geometric series below, or indicate that the sum does not exist. 15+6+12/5+24/25+...

asked by Elise on February 26, 2017
65. ## Algebra

find the sum of the infinite geometric series 1/3+1/9+1/27 sum=a_1/1-r

asked by Keonn'a on September 28, 2018
66. ## Math

1. Find the 11th term of the geometric sequence 64, -32, 16, -8, … . 2. Find the 1st term of a geometric sequence with a 10th term -1024 and r = -2. 3. Find the sum of each infinite geometric series, if possible. a. 10 + 2 + 2/5 + ..... b. 1.2 – 2.4 +

asked by Brianna on October 7, 2014
67. ## math

The 65th therm in a geometric sequence is 8000, and the 69th term is 500, find the 64th term using the geometric series sum formula

asked by Poppy on December 18, 2011
68. ## Algebra

Two questions I need help with. Find the indicated partial sum using the information given. 1. a3=4/9, a7=9/64, S6 Determine wheater the infinite geometric series has a finite sum 2. 6+ 3+ 3/2 + 3/4 +.... 3. -49 + (-7) + (- 1/7) +...

asked by Becca on April 8, 2013
69. ## calculus

find the sum of the series from n=1 to infinity of 2^n/n! do I just look at the sum of the terms?

asked by sarah on March 20, 2008
70. ## Math

The first term of geometric is 124.the sum of infinity is 64.find the common ratio

asked by Ludere tshifularo on March 28, 2015
71. ## Math

The sum to infinity of a G.P. is 16 and the sum of the first 4terms is 15. Find the first 4 terms. Find the sum to infinity of the following (if they converge). ?(a)4+4/3+4/3²+... (b)9+7+5+3+...(can't do, its an AP ?) (c)20-10+5-2.5+...a=20,r=-0.5

asked by Anonymous on April 21, 2008
72. ## calc

does the sum of [(-5)^n]/[13^(n+1)] converge? as n goes to infinity I think that since it oscillates it does not go to infinity. and therefore the series diverges.

asked by lola on February 1, 2012

Find the sum to infinity of the series 1 + 4/3! + 6/4! + 8/5!

asked by Ben on May 2, 2015

Find the sum to infinity of the series 1 + 4/3! + 6/4! + 8/5!

asked by Ben on May 2, 2015
75. ## Math

1/27 + 1/9 + 1/3 + ... + 81 I know the series is geometric. d = 1/3 Multiplying each by 1/3 to get the next value do i use the sum of geometric series a(1-r^n)/ 1-r

asked by Tasha on December 12, 2014
76. ## Calc 2

find the sum of the series: sum from k=1 to infinity [(3/k(k+1)(k+2))+(-2/3)^k]

asked by chelsea on April 16, 2014
77. ## calculus

true or false: if the sum from n=1 to infinity of a(n) converges, and the sum from n=1 to infinity of b(n) diverges, then the series from n=1 to infinity of (a(n)*b(n)) diverges i said this was true... is this correct?

asked by sarah on February 24, 2008
78. ## Math

Find the sum of the geometric series. 10 1. Ó 5(2)^i - 1 i= 1 12 2. Ó 8(3/2)^i - 1 i= 1

asked by Neil on May 23, 2012
79. ## ALG 2

27 + 9 + 3... Find the sum of the geometric series given

asked by Embraced on January 14, 2012
80. ## sum geometric series

what is the sum of geometric infinite series 3/2+ 9/16+ 27/128+ 81/1024=.... i know the formula is S=a/(1-r) my teacher, he usually transforms into a formula of the sum series and finds out a and r.but i don't how to do that. the pattern i saw is 3/2 +

asked by david on April 9, 2007
81. ## Math

Geometric series: n= infinity sign a1=5 r= -1/4 The equation 5(-1/4)^i-1

asked by Aria on June 2, 2017
82. ## Math

4) The sum of an infinite geometric series is 100. The second term of the series is 24. Find two possibilities for a (the first term) and r (the common ratio). b. Given, 5 2 4 a a a    159 and 4 1 3 a a a    265 , find the terms of the

asked by Susan on September 21, 2016
83. ## Induction

Given the series 1,2,3,4,5,10,20,40,80,..... which starts as an arithmetic series for the first five terms and then follows geometric series. It can be proved by strong induction that any positive integer can be written as a sum of distinct numbers of this

asked by bcruga on September 28, 2017

find sum of the first 10terms of geometric series with a2=1/2 and r=2

asked by Anonymous on May 7, 2012

find sum of the first 10terms of geometric series with a2=1/2 and r=2

asked by Anonymous on May 7, 2012
86. ## Algebra 2

How would I find the sum of the geometric series given? 1/5 - 1/25 + 1/125

asked by Greg on May 12, 2012
87. ## Algebra

Find the sum of the infinite geometric series given by ∑_(k=1)^∞〖(2/9)^k〗

asked by Jessica on August 4, 2010
88. ## Algebra 2

5+(-5/2)+(5/4) Sn=189 Find n for the given sum if the geometric series

asked by Rachel on May 7, 2012
89. ## College Algebra

Find the sum of the infinite geometric series given by ∑_(k=1)^∞▒〖(2/9)^k.〗

asked by Jessica on August 9, 2010
90. ## Algebra

find the sum of the infinite geometric series 4+1+1/4+...

asked by Keonn'a on September 28, 2018
91. ## Algebra 2

How do you find the sum of the infinite geometric series: a1 = -5, r = 1/6?

asked by Nikki on November 5, 2017
92. ## Math

Find the sum of a geometric series for which a1=1,r=2,and n=6. Sn=a1(1-r^n)/1-r S6=1(1-2^6)/1-2 S6=1(1-64)/1-2 S6=63/1 63 (answer)

asked by Jon on March 4, 2008
93. ## math

find the sum of the first 10 terms of geometric series with a[2]=(1)/(2) and r=2

asked by Anonymous on May 3, 2012
94. ## math B30

If the seventh term of a geometric series is 192, and the first term is 3, find the sum of the first 8 terms of the series

asked by alix on June 15, 2010
95. ## calculus infinate sums

how many terms of the series 1/(n*(ln(n)^8)) from n=2 to infinity would you have to add to find the sum to within 0.01

asked by johnathon on September 11, 2011
96. ## Maths - Geometric Progression

The second term of a GP is 1/2 and the sum ti infinity of the series is 4. Find the first term and and the common ratio of the series.

asked by Anonymous on September 25, 2012
97. ## Math

I have a couple questions about the sums of geometric series. One. So the formula for the sum is t(n)=t(1)[(r^n)-1] But if my series starts at t(0), can I change the formula to t(n)=t(0)[(r^n)-1] ? Two. If, in the series, there is a different pattern in

asked by Anonymous on October 31, 2010
98. ## MATHEMATICS

If x>1 find the sum of infinity of x ^2/(x-1)+x+(x-1).... And also find the value of x for the given series TO HAVE THE SUM OF INFINITY

asked by CHARLES BRONSON on March 6, 2014
99. ## algebra, series

The sum of the first n terms of a series is 1-(3/4). Obtain an expression for the nth term of the series. Prove that the series is geometric, and state the values of the first term and the common ratio. Please show workings

asked by youngguru on March 15, 2017
100. ## college precalculus

find the sum of the infinite geometric series 1/3^6+1/3^8+1/3^10+1/3^12........ -100/9+10/3-1+3/10

asked by fred on May 1, 2015