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

Given P(n):3^(2n) -1 is divisible by 8. If P(k) is true then prove P(k+1) is true.

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

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

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

Consider the statement '' P(n):x^n-y^n is divisible by x-y ''. Show that P(1) is true.

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

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

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.