prove the following by mathematical induction:- 10^2N-1+1 IS DIVISIBLE BY 11

Hi!

Let p(n) be 10^2n-1+1 =11p

p(1) = 10+1 = 11 which is divisible by 11

Let p(k) be true.

p(k) = 10^2k-1+1 = 11m

p(k+1) = 10^{2(k+1) - 1}+1

=10^2k+2-1+1

=10^2k-1.10²+1

=11m . 10²

which is a multiple of 11.

Hence by principle of mathematical induction, p(n) is true for all n ∈ N