1. ## Series Divergence/Convergence

Need some help with this question

does the series

Sum of $\displaystyle \frac{2^n}{n^2}$ from n=1 to infinity

i've tried ratio test method and end up with 1/2 which says the series converges but this series apparently diverges..

2. Originally Posted by Kevlar
Sum of $\displaystyle \frac{2^n}{n^2}$ from n=1 to infinity
i've tried ratio test method and end up with 1/2 which says the series converges but this series apparently diverges..
Ratio: $\displaystyle \frac{a_{n+1}}{a_n}$.

3. ahhh yeh i got it now i got 2 which is >1 therefore divergent

4. As a matter of fact, for some "n" will get that the numerator is bigger than the denominator, hence the divergence is obvious.

5. Originally Posted by Kevlar
Need some help with this question

does the series

Sum of $\displaystyle \frac{2^n}{n^2}$ from n=1 to infinity

i've tried ratio test method and end up with 1/2 which says the series converges but this series apparently diverges..

Excause me, Do you know the nth term test ?