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):x^n-y^n is divisible by x-y ''. 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):7^n-3^n is divisible by 4. Show that P(1) is true.

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

Let P(n) denotes the statement 10^(2n-1)+1 is divisible by 11. If P(m) is true, prove that P(m+1) is also true.

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

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

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.

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