Let P(n):1+3+5+……+(2n+-1)= n^'2(i)Verify P(1) is true.

Let P(n):1+3+5+……+(2n+-1)=n'^'2(ii)Write P(k).

Consider the statement P(n)=1+3+3^2+….+3^(n-1)=(3^n-1)/2 (b)If P(k) is true,prove that P(k+1) is also true.

Consider the statement P(n):1x2+2x3+3x4+………+n(n+1)='(n(n+1)(n+2)/3' (a)Verify that P(3) is true.

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

If P(n) is the statement '4n<2^n'(iii)If P(K) is true,show that P(K+1) is true for Kge5 .

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.

A statement p(n) for a natural number n is given by p(n):1/2+1/4+1/8+…….+1/2^n=1-1/2^n Verify that p(1) is true.

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)=1+3+3^2+…….+3^(n-1)=frac(3^(n-1))(2) Check P(1) is true.

Consider the statement P(n)=1+3+3^2+…….+3^(n-1)=frac(3^(n)-1)(2) If P(k) is true, prove that P(k+1) is true.