For the following, decide whether $T(n)=(f(n)),T(n)=(f(n)),T(n)=O(f(n)),$ or none

of the above. Justify your answers.

$($a$)T(n)=(n+1)!,f(n)=n!.$

$($b$)T(n)=2^{logn},f(n)=n^{\frac{1}{logn}}.$

$($c$)T(n)=n,f(n)=(logn{)}^{10}.$

$($d$)T(n)={\displaystyle \underset{i=1}{\overset{n}{}}}{3}^i,f(n)=3^{n-1}.$