If `n | k` denotes k is divisible by n then prove by induction, that `512|(3^(2n +5) + 160n^2 - 56n – 243)` for all `n in N`.

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

Prove by induction that : 2^(n) gt 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.

Prove by induction that the sum S_n=n^3+3n^2+5n+3 is divisible by 3 for all n in Ndot

Prove by Induction, for all n in N : 2^n >n .

By method of induction, prove that 5^(2n) - 1 id divisible by 6, for all n in N .

Prove by induction that n(n+1) (2n+1) is divisible by 6.

Using mathemtical induction prove that 3^(2n + 2)- 8n - 9 is divisible by 64 for all n in N .

Prove,by induction,that 8*7^(n)+4^(n+2) is divisible by 24 but not by 48 for all n in N in N in N

Prove by Induction, that (2n+7)le (n+3)^2 for all n in N. Using this, prove by induction that : (n+3)^2 le 2^(n+3) for all n in N.