Prove by induction that `4+8+12++4n=2n(n+1)` for all `n Ndot`

Prove by induction that 4+8+12++4n=2n(n+1) for all nN.

Prove by induction that : 2^(n) gt n for all n in N .

Prove, by Induction, that 2^(n)ltn! for all nge4

Prove,by induction,that 3^(n)>n for all n in N

Prove by induction that the sum S_(n)=n^(3)+2n^(2)+5n+3 is divisible by 3 for all n in N.

Using the principle of mathematical induction, prove that n<2^(n) for all n in N

Using the principle of mathematical induction prove that (1+x)^(n)>=(1+nx) for all n in N, where x>-1

Prove by the principle of mathematical induction that n(n+1)(2n+1) is divisible by 6 for all n in N

Prove by principle of Mathematical Induction that for all natural number in n(n+1)(n+2) is divisible by 6.

Prove by induction that the integer next greater than (3+sqrt(5))^n is divisible by 2^n for all n in N .