Use the informal definitions of $O,,$ and $$ to determine whether the follow$-$

ing assertions are true or false.

a$.n\frac{n+1}{2}$inO$(n^3)$

b$.n\frac{n+1}{2}$inO$(n^2)$

c$.n\frac{n+1}{2}in(n^3)$

d$.n\frac{n+1}{2}in(n)$