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Convergence of a Series

  • #1
[tex]\sum_{k=1}^{\infty}\frac{2+\left(-1 \right)^{k}}{5^{k}}[/tex]

Hello, I am trying to determine if this series converges or diverges. I have tried comparison test and d'Alembert's test but I was not successful

Can anyone suggest me a test learned in Calculus 2 that will work?

Thank you
 

Answers and Replies

  • #2
392
0
Break it into a sum of two series?
 
  • #3
Cyosis
Homework Helper
1,495
0
Since you're asking if there exists another test you could also use.

[tex]
\lim_{n \to \infty}\sqrt[n]{|a_n|}<1
[/tex]

It converges absolutely if the limit is smaller than 1.
 
  • #4
Thank you, I have figured it out. I have another question if you don't mind

[tex]\sum_{k=1}^{\infty}\frac{\left|\cos k \right|}{k^{3}}[/tex]

It looks like a riemann series but I don't really know how to deal with trigonometric functions in series yet. What to do? Can anyone explain me?

Thank you
 
  • #5
614
0
What values can |cos k| take? Perhaps consider a p-series
 

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