Exercise $3.$

The given sequence is:

$c_n=\frac{ln(n)}{n^p}$

converges or diverges for $p>1.$ If it converges, find its limit$.$

$2.$ Determine whether the series

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{ln(n)}{n^p}$

converges or diverges for $p>1.$

$3$

Hint

Use the Integral Test.

Use the integration by substitution.