$($i$)$ What do you mean by conditionally convergent series? Give an example.

Prove that the series

$2-\frac{3}{2}+\frac{4}{3}-\frac{5}{4}+$dots

is divergent.

$1+1+3$

$($ii$)$ State the Integral test for convergence of an infinite series. Use this test to show that the series ${\displaystyle \underset{n=2}{\overset{}{}}}\frac{1}{n(logn{)}^p}(p$ is a positive real number$)$ converges for $p>1$ and diverges for $p1.$

$1+4$