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Help with understanding this series

Linus12351

New member
Mar 26, 2020
1
Can anyone help with this problem. I've tried integral test but seems to be too complicated.pleasehelp.PNG
 

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,100
The Astral plane
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
Jan 26, 2012
1,403
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.