For all `nge1`, prove that `p(n):n(n+1)(n+5)` is divisible by 3.

For all nge1 , prove that p(n):n^3+(n+1)^3+(n+2)^3 is divisible by 9.

For all nge1 , prove that p(n):2.7^n+3.5^n-5 is divisible by 24.

For all nge1 , prove that p(n):2^(3n)-1 is divisible by 7.

(a) P(n):n(n+1)(n+2) is divisible by 6,then find P(3) .

Prove 'that 10^n+3 xx 4^(n+2)+5 is divisible by 9 .

(a)Prove that 3^(2n)-1 is divisible by 8.

Using binomial thẹorem, prove that 3^(3 n)-26 n-1 is divisible by 676 , where n in N

Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. Verify the statement for n=2.

Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assume that P(k) is true for a natural number k, Verify that P(k+1) is true.

By mathematical induction prove that the statement 3^(4n+1)+2^(2n+2) is divisible by 7 is true for all n in N