Prove by induction that $10^n -1$ is divisible by 11 for every even natural number n. $0 \notin N$
Base Case: n = 2, since it is the first even natural number. $10^2 -1 = 99$ which is divisible by 11.
Assume $n =k $ is true for some $k \in N$. Now prove $n=k+1$ is true.
I know I have to put k+1 instead of k, but I do not know how to relate the induction hypothesis with k+1.