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)=3^(2n+2)-8n-9 is divisible by 8 Verify the statement for n=1.

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.

Consider the statement P(n):2^(3n) -1 is divisible by 7 Is the statement p(1) true? justify your answer

Consider the statement P(n):7^n-3^n is divisible by 4. Verify, by the method of mathematical induction, that P(n) is true for all natural numbers.

Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Prove the statement using the principle of mathematical induction for all natural numbers.

Consider the statement '' 10^(2n-1)+1 is divisible by 11''. Verify that P(1) is true and prove the statement by using mathematical induction.

Consider the statement P(n):7^n-3^n is divisible by 4. Show that P(1) is true.

Consider the statement '' 7^n-3^n is divisible by 4'' Verify the result for n=2 .

Consider the statement P(n):2^(3n) -1 is divisible by 7 If p(k) is true, show that p(k+1) is also true

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