By method of induction, prove that `2^n > n`, for all `n in N`.

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

By method of induction prove that 1+2+3+...+n = (n(n+1)) /2, for all n in N

By method of induction, prove that 1.6 + 2.9 + 3.12 +... +to n terms = n(n +1 )(n+2) for all n in N .

By method of induction prove that 1.3 + 2.5 + 3.7 +...+ n (2n + 1) = n/6 (n + 1) (4n + 5) for all n in N

By method of induction, prove that sum_(r=1)^n ax^(r-1) = a ((1-x^n)/(1-x)) , for all n in N , x != 1 .

Prove, by method of induction, for all n in N : 2 + 3.2 +4.2^2 +...+ (n + 1) (2^(n-1)) = n.2^n

Prove, by method of induction, for all n in N : 8 + 17 + 26 +...+ (9n - 1) = n/2 (9n + 7)

Prove, by method of induction, for all n in N : 1^2 + 4^2 + 7^2 +...+ (3n - 2)^2 = n/2 (6n^2 - 3n - 1)

Prove the following by the method of induction for all n in N : (cos theta + i sin theta)^n = cos n theta + i sinntheta , where i = sqrt -1.

Prove the following by the method of induction for all n in N : 2 + 4 + 6 +... +2n = n(n + 1).