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

[tex]

\sum_{k=2}^\infty \frac{k^2}{k^2-1}

[/tex]

[tex]

\sum_{n=1}^\infty \frac{1+2^n}{3^n}

[/tex]

2. Relevant equations

I know that for the first problem i can apply the Divergence test by finding my limit as K goes to infinity. By doing this i get 1 which does not equal zero so i know it diverges.

Now my question is why cant i apply this same test to the 2nd problem? it seems as n approaches infinity i would get 1 as well. but thats not the case the correct solution for the 2nd problem is as follows..

[tex]

\sum_{n=1}^\infty \frac{1}{3^n} + \frac{2^n}{3^n}

[/tex]

Then by using a little algebra and sum of two convergent geometric series we get 5/2 to be the answer. which is convergent.

So why cant i find my limit as n approaches infinity in the 2nd problem? and why is 5/2 convergent? i thought if r>1 the series diverges?

Any help is appreciated.

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

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!

# Infinite series problem

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