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

(b) P(n):7^n-3^n is divisible by 4,then find P(2) .

(b) P(n):5^(2n+2)-24n-25 is divisible by 576,then P(0)=………..

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

Let P(n) : n(n+1)(n+2) is divisible by 6. Determine whether the statement is true or false, when n=3 and n=5. Justify your answer.

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.

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

If P(n) is the statement n(n+1)(n+2) is divisiblé by 12, prove that P(3) and P(4) are true, but P(5) is not true

Given P(n):3^(2n) 1 is divisible by 8. Is the statement P(n) true for all natural numbers? Justify your answer.

Given P(n):3^(2n) -1 is divisible by 8 Check whether P(1) is true.