$a.$ Suppose that ${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ and ${\displaystyle \underset{?}{\overset{?}{}}}{b}_n$ are series with positive terms and ${\displaystyle \underset{?}{\overset{?}{}}}{b}_{n}is$

convergent. Prove that $if$

$\underset{n}{lim}\frac{a_n}{b_n}=0$

then ${\displaystyle \underset{?}{\overset{?}{}}}{a}_{n}is$ also convergent.

$b.$ Use part $(a)to$ show that the series converges.

$i.,{\displaystyle \underset{n=1}{\overset{}{}}}\frac{lnn}{n^3}$

$ii.,{\displaystyle \underset{n=1}{\overset{}{}}}(1-cos(\frac{1}{n_2}))$