# Algebra

For the geometric series given by 2+4+8+... , which of the following statements is FALSE?

Select one:

a. S200>S199

b. S200>a200

c. S1=a1

d. None of the other 3 statements here are False.

1. 👍
2. 👎
3. 👁
1. In a geometric sequence:

an = a1 ∙ rⁿ⁻¹

Sum of the first n terms of a geometric sequence:

Sn = a1 ∙ ( 1 − rⁿ ) / ( 1− r )

where

a1 = first term

r is the common ratio

In tis case

a1 = 2 , r = 2

so

Sn = a1 ∙ ( 1 − rⁿ ) / ( 1− r )

S199 = 2 ∙ ( 1 − 2¹⁹⁹ ) / ( 1− 2 )

S199 = 2 ∙ ( 1 − 2¹⁹⁹ ) / ( - 1 )

S199 = - 2 ∙ ( 1 − 2¹⁹⁹ ) = 1.6069380442589902755419620923412 ∙ 10⁶⁰

S200 = 2 ∙ ( 1 − 2²⁰⁰ ) / ( 1− 2 )

S200 = 2 ∙ ( 1 − 2²⁰⁰ ) / ( - 1 )

S200 = - 2 ∙ ( 1 − 2²⁰⁰ ) = 3.2138760885179805510839241846823 ∙ 10⁶⁰

S200 > S199

3.2138760885179805510839241846823 ∙ 10⁶⁰ > 1.6069380442589902755419620923412 ∙ 10⁶⁰

True

an = a ∙ rⁿ⁻¹

a200 = 2 ∙ 2¹⁹⁹ = 2²⁰⁰ = 1.6069380442589902755419620923412 ∙ 10⁶⁰

S200 > a200

3.2138760885179805510839241846823 ∙ 10⁶⁰ > 1.6069380442589902755419620923412 ∙ 10⁶⁰

True

S1 = a1

2 = 2

True

d. None of the other 3 statements here are False.

1. 👍
2. 👎

## Similar Questions

1. ### 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

2. ### Calculus

Which one of the following statements is true about the series the series from n equals 1 to infinity of the quotient of negative 1 raised to the nth power and n ? (4 points) Is this A or B? I am a little confused. A) It is

3. ### 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} • r^(n – 1) = a{1} ⁄ (1 – r)

4. ### Calculus

Consider the series 1/4+1/6+1/9+2/27+4/81+.... Does the series converge or diverge? Is the series arithmetic, geometric, neither, or geometric with an absolute value of the common ration being greater/ less than 1?

1. ### Algebra

Is the series 72, 48, 32,... an arithmetic or geometric series. WHat is common difference or ratio

2. ### math

in a geometric series t1=23,t3=92 and the sum of all of the terms of the series is 62 813. how many terms are in the series?

3. ### Calculus

Which of the following statements is true? (4 points) A) The nth term test can never be used to show that a series converges. B) The integral test can be applied to a series even if all the terms are not positive. C) The series

4. ### 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

1. ### Calculus

Which of the following statements is true for the series the summation from k=1 to infinity of the sin(k)/k^2? (10 points) A) The series converges conditionally but not absolutely. B) The series is divergent. C) The series cannot

2. ### math

The sum of the 1st nine terms of an arithmetic series is 216. The 1st,3rd and the 7th terms of series form the 1st three terms of a geometric series. Find the 1st term and the constant difference of the arithmetic series ?

3. ### algebra

Consider the infinite geometric series below. a. Write the first 4 terms of the series b. Does the series diverge or converge? c. If the series has a sum, find the sum. infinity sigma n=2 (-2)^n-1

4. ### Calculus

Which of the following statements is/are true about the series the summation from n=0 to infinity of (3/2)^n? I. It diverges. II. It is geometric. III. It is arithmetic Possible answers: a) I only b) II only c) I and II only d) I