Help with understanding this series

Linus12351

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

topsquark

Well-known member
MHB Math Helper
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

Prove It

Well-known member
MHB Math Helper
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.