
#1
March 26th, 2020,
19:52
Can anyone help with this problem. I've tried integral test but seems to be too complicated.

March 26th, 2020 19:52
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#2
March 26th, 2020,
20:42
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

#3
March 26th, 2020,
21:24
Originally Posted by
Linus12351
Can anyone help with this problem. I've tried integral test but seems to be too complicated.
Easy,
$\displaystyle 0 \leq \sum{\frac{1}{5^{n1} + 1}} < \sum{\frac{1}{5^{n1}}} = \sum{ \left( \frac{1}{5} \right) ^{n1} }$
Since your positive term series is less than a convergent geometric series, your series converges by comparison.