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 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 2^n > n , for all n in N .

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

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

Prove the following by the method of induction for all n in N : 1^2 + 3^2 + 5^2 + ... + (2n - 1)^2 = n/3 (2n -1) (2n +1)

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

Prove the following by the method of induction for all n in N : 1.2 + 2.3 + 3.4 +...+ n(n + 1) = n/3 (n+1)(n+2).

Prove the following by the method of induction for all n in N : 1^2 + 2^2 + 3^2 + ... + n^2 = (n(n + 1) (2n + 1)) / 6 .

Prove 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1), AA 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 .