Prove the following by the method of induction for all `n in N`: `(2^(4n) -1)` is divisible by 15.

Prove the following by the method of induction for all n in N : (2^(3n) -1) is divisible by 7.

Prove the following by the method of induction for all n in N : 3^n - 2n - 1 s divisible by 4.

Prove the following by the method of induction for all n in N : 2 + 4 + 6 +... +2n = n(n + 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 : Given t_(n+1) = 5t_(n+4), t_1 = 4. P.T t_n = 5^(n -1)

Prove the following by the method of induction for all n in N : 5 + 5^2 + 5^3 + .. + 5^n = 5/4 (5^n - 1)

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 + 3^2 + 5^2 + ... + (2n - 1)^2 = n/3 (2n -1) (2n +1)

Prove the following by the method of induction for all n in N : 1/1.3 + 1/3.5 + 1/5.7+...+ 1 / ((2n-1)(2n+1)) = n / (2n+1)

49^n + 16n -1 is divisible by