# Thread: Help with understanding this series

1. Can anyone help with this problem. I've tried integral test but seems to be too complicated.

2.

3. Originally Posted by Linus12351
Can anyone help with this problem. I've tried integral test but seems to be too complicated.
Have you tried looking at $\displaystyle \lim_{n \to \infty} \dfrac{a_{n + 1}}{a_n}$?

-Dan

4. Originally Posted by Linus12351
Can anyone help with this problem. I've tried integral test but seems to be too complicated.
Easy,

$\displaystyle 0 \leq \sum{\frac{1}{5^{n-1} + 1}} < \sum{\frac{1}{5^{n-1}}} = \sum{ \left( \frac{1}{5} \right) ^{n-1} }$

Since your positive term series is less than a convergent geometric series, your series converges by comparison.