$($a$)$ For a constant $c>0,$ the solution of $T(n)=T(4\frac{n}{7})+T(3\frac{n}{7})+cn$ is

$O(nlogn).$

$($b$)$ The solution of $T(n)=2T(\frac{n}{2})+\frac{n}{logn}$ is $(nloglogn).($Hint: The $k-$th

harmonic number, $H_k$ is defined as $\{$:$H_k=(logk))H_k={\displaystyle \underset{?}{\overset{?}{}}}$