Series Convergence

Welcome to the Series Convergence category on Questions LLC! Whether you are a math enthusiast or a student studying calculus, this category is the perfect place for you to dive into the fascinating world of series convergence. Here, you will find a plethora of questions, discussions, and insights surrounding the convergence and divergence of various types of series. From power series to geometric series and everything in between, our dedicated community of experts and enthusiasts is here to help unravel the mysteries of series convergence. So, whether you are seeking clarification, looking for step-by-step solutions, or simply curious about the topic, come on in and explore the vast knowledge shared by our community in the Series Convergence category.

Questions (71)

Which of the following series converge?A. 1 + 1/2^2 + 1/3^2 + ... + 1/n^2 + ... B. 1 + 1/2 + 1/3 + ... + 1/n + ... C. 1 - 1/3 +
1. 4 answers
2. asked by Anonymous
3. 2,262 views
how is this series 3+ 9/4 +27/16 +81/64... is converge to 12?i represent the series as 3^(n+1)/4^n n starts from 0 to infinity,
1. 4 answers
2. asked by eng
3. 1,657 views
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.Does the series converge
1. 7 answers
2. asked by kiki
3. 155 views
Determine if series is absolutely convergent, conditionally convergent or divergent.(-1)^(n-1) *(9^n)/(n^8)
1. 2 answers
2. asked anonymously
3. 91 views
Evaluate the geometric Series or state that it divergeslower bound k= 1 upper bound = infinity E (sum symbol) E 5(-1/6)^(5k) I
1. 3 answers
2. asked by Kate
3. 1,607 views
Where does this infinite series converge:Sigma (k = 1 to infinity): 1/(9k^2 + 3k - 2)
1. 7 answers
2. asked by Sean
3. 3,422 views
Consider the series∑ ∞ n=1 (13/10^n) Determine whether the series converges, and if it converges, determine its value.
1. 4 answers
2. asked by maggie
3. 1,794 views
determine if the series converges or diverges:1/(ksqrt(k^2+1)) from k = 1 to infinity
1. 6 answers
2. asked by anonymous
3. 1,040 views
For what values of k does the series ∑n=1 to infinity (11/(2k^2 + 3))^n converge?I think this is k < -2 and k > 2.
1. 4 answers
2. asked by Anonymous
3. 2,904 views
Show that the series(−1)^n−1(bn) where bn = 1/(n^1/2) if n is odd and bn = 1/2^nif n is even, diverges. Why does the
1. 7 answers
2. asked by amber
3. 641 views
Which of the following series is NOT absolutely convergent?A. the summation from n equals 1 to infinity of the quotient of
1. 3 answers
2. asked by kaa
3. 730 views
Which one of the following statements is true about the series the series from n equals 1 to infinity of the quotient of
1. 3 answers
2. asked by Lia
3. 1,434 views
Determine whether the infinite series,sigma(((-1)^(n+1))/n)^2 converges or diverges. My professor gave these in a problem set
1. 4 answers
2. asked by Ashley
3. 1,007 views
Use Theorem 9.11 to determine the convergence or divergence of the p-series.1+ 1/6root2 + 1/6root3 + 1/6root4 +... p=
1. 1 answer
2. asked by Maria
3. 299 views
determine whether the given series converges or divergesseries inf, n=1 (4n/(n+400))^n
1. 1 answer
2. asked by Ricky
3. 201 views
determine whether the given series converges or divergesseries inf, n=1 4n/(n^2+400)
1. 1 answer
2. asked by Ricky
3. 194 views
Determine whether series converges inf, n=1 4n/(n^2+400)I know that the series diverges, need steps
1. 1 answer
2. asked by Antonette
3. 283 views
Show whether the series ((-1)^n)*((2^n)/(n^4))) is absolutely convergent.Taking an=((-1)^n)*((2^n)/(n^4))) , here
1. 1 answer
2. asked by Ashley
3. 352 views
Test the series for convergence or divergence.∑from n=1 to ∞ ((e^n) /n^2)what test should I use?
1. 1 answer
2. asked by Anonymous
3. 375 views
For what values of p is this series convergent?(summation from n = 1 to infinity) of ((-1)^(n-1))/(n^(p + 2)) A. p >= -2 B. p
1. 3 answers
2. asked by Joeseph
3. 677 views
Determine whether the series is convergent or divergentseries symbol n=1 to infinity (n^2/(e^(3n))
1. 3 answers
2. asked by TayB
3. 1,228 views
Find if series is convergent or divergent.Series from n=2 to infinity (4n+7)/(3n^3 -8n)
1. 1 answer
2. asked by John
3. 447 views
Use the Comparison Test to determine whether the series is convergent or divergent.On top of the summation sign (∑) is
1. 2 answers
2. asked by Sena
3. 498 views
Determine whether the p-series is convergent or divergent.On top of the summation sign (∑) is infinity. Under the summation
1. 4 answers
2. asked by Sena
3. 496 views
Can anyone help me start this problem from beginning to end, along with explanations on how to go about the problem for a better
1. 3 answers
2. asked by Sena
3. 616 views
Show that the series 1 + 2x/5 + 3x^2/25 + 4x^3/125 + ....is convergent if -5<x<5 and for no other value of x.
1. 1 answer
2. asked by tolu
3. 378 views
state whether the series is convergent or divergent1) 3 + 12 + 48 + ... 2) 4 + 4/5 + 4/25 + ...
1. 3 answers
2. asked by Eric
3. 390 views
In the following series x is a real number. In each case, use the ratio test to determine the radius of convergence of the
1. 1 answer
2. asked by BAE
3. 475 views
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
1. 2 answers
2. asked by Bae
3. 510 views
Is the series convergent or divergent?n=1 series to infinity (-1)^n * (sqrt(n)/(4+5sqrt(n)) Does this diverge?
1. 1 answer
2. asked by James
3. 440 views
Does3/4 - 3/5 + 3/6 - 3/7 + 3/8.... Converge or Diverge?
1. 1 answer
2. asked by James
3. 339 views
Find the radius of convergence and interval of convergence of the series.n=2 series to infinity (-1)^n * x^n+6/n+7 R= ? I= (or[
1. 2 answers
2. asked by James
3. 530 views
n=1 series to infinity (-5^n)/n^3 does it absolutely converge, diverge or conditionally converge. Would I be applying the ratio
1. 4 answers
2. asked by James
3. 728 views
The question is: n=0 E to infinity 4+sin(n)/3^nDoes it converge or diverge? i'm doing this hw problem and I believe it converges
1. 1 answer
2. asked by James
3. 371 views
determine whether the series 1 + 1/2^5 + 1/3^5 + 1/4^5 +...is convergent or divergent?How do I tell the difference?
1. 3 answers
2. asked by What's the Difference?
3. 417 views
use integral test to determine whether the series is convergent or divergentinfinity (sum symbol) n=1 1/(sqrt n)^5
1. 1 answer
2. asked by Jessica
3. 474 views
Is this correct?determine if absolutely convergent and convergent 1. the series from n=0 to infinity of ((-1)^n)/n! I said it
1. 1 answer
2. asked by john
3. 367 views
we know the series from n=0 to infinity of c(sub n)*3^n converges1. TRUE OR FALSE the series from n=0 to infinity of c(sub
1. 1 answer
2. asked by jane
3. 428 views
infinity of the summation n=1: (e^n)/(n!) [using the ratio test]my work so far: = lim (n->infinity) | [(e^n+1)/((n+1)!)] /
1. 1 answer
2. asked by COFFEE
3. 1,035 views
Determine the convergence of the following series using the nth-partial sum or geometric series formula.The sum of n=1 to
1. 1 answer
2. asked by Ace
3. 800 views
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
1. 1 answer
2. asked by Mischa
3. 681 views
Match each series to the test that should be used to test for convergence/divergence. While it is possible that each test could
1. 2 answers
2. asked by Clara
3. 925 views
Determine the convergence or divergence of the series. Indicate the test that was used and justify your answer.Sigma (lower
1. 1 answer
2. asked by Jenny
3. 901 views
Does the series (1+sin(n))/(10^n) from summation 0 to positive infinity converge or diverge?I let an = (1+sin(n))/(10^n) and bn
1. 2 answers
2. asked by Joshua
3. 894 views
determine if the series is absolutely convergent and convergentthe sum from n=1 to infinity of sin(n^2)/n^2 what series test
1. 2 answers
2. asked by sarah
3. 879 views
determine whether the series converges of divergesthe sum from k=1 to infinity of cos(e^-k) I'm not sure where to start..
1. 2 answers
2. asked by sarah
3. 827 views
Which one of the following series is convergent?A. the summation from n equals 1 to infinity of 1 over the quantity n squared B.
1. 3 answers
2. asked by kaa
3. 751 views
State the convergence/divergence for the series the summation from n equals 1 to infinity of the product of negative 1 raised to
1. 2 answers
2. asked by Tess
3. 648 views
Which of the following series converges conditionally? (4 points)A) the summation from n equals 1 to infinity of the quotient of
1. 1 answer
2. asked by Tess
3. 639 views
Consider∞ ∑ [(3k+5)/(k²-2k)]ᵖ, for each p ∈ ℝ. k=3 Show this series { converges if p > 1 { diverges if p ≤ 1 Hint:
1. 2 answers
2. asked by Bernie
3. 652 views

Series Convergence

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