Given sets $A,B$ and $C,$ simplify $(A(B-C))(C-(AB)).$

Given a finite set $A,$ prove that if a function $f$:$AA$ is not injective, then $f$ is not surjective.

Given integer $n,$ prove that $3|$~$\frac{n}{3}$~$|n+2.$

Evaluate ${\displaystyle \underset{k=1}{\overset{n}{}}}{2}^{n(1+k)}.$

Evaluate ${\displaystyle \underset{k=1}{\overset{n}{}}}\frac{k}{(k+1)((k+1{)}^2-1)}.$