Prove the `2^(n)+6times9^(n)` is always divisible by 7 for any positive integer n.

Prove that n + n is divisible by 2 for any positive integer n.

Prove that 7^(n) - 6n - 1 is always divisible by 36.

Prove that n^(2)-n is divisible by 2 for every positive integer n.

Using binomial theorem for a positive integral index, prove that (2^(3n)-7n-1) is divisble by 49, for any positive integer n.

Prove that n^(2)-n divisible by 2 for every positive integer n.

Prove that n^(2)-n divisible by 2 for every positive integer n.

Prove that n^2-n divisible by 2 for every positive integer n.

Prove,by mathematical induction,that x^(n)+y^(n) is divisible by x+y for any positive odd integer n.

Using binomial theorem, prove that 50^(n)-49n-1 is divisible by 49^(2) for all positive integers n.

For + ve integer n,n^(3)+2n is always divisible by