I have attached the question.

I have expanded $\displaystyle (1+h)^n$ using the binomial theorem, and the question after it I assume they want me to use the very same theorem to prove the convergence.

So this is what I had done;

$\displaystyle (n+1)^{1/n}=1+h \rightarrow n+1=(1+h)^n=1+nh+\frac{n!}{2!(n-2)!}+...+h^n$

I'm not sure how to prove convergence from then on, but I am guessing the Sandwich Rule would need to be used here at one point.

Any hints/tips?