(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi everyone ,, got the following question

Sum(k=1,infinity) (2009+5^(-k^3))/(k^2(1+e^(-k^2)))

2. Relevant equations

3. The attempt at a solution

first I think it diverges so I did a comparison which is :

ak = (2009+5^(-k^3))/(k^2(1+e^(-k^2)))

e^(k^2))/(5^(k^3)*k^2) which is less than ak ,,

but now what should I do ?? which test should I use to make it diverges (that is if it diverges)

note : I tried already ratio test and it didn't work and k-th term but I get (infinity over infinity) so it's no use ,, can someone help please

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Deciding if the series converges or diverges

**Physics Forums | Science Articles, Homework Help, Discussion**