# Proof of convergence

by disregardthat
Tags: convergence, proof
 Sci Advisor P: 1,807 How can we prove that $$n^s-(n-1)^s$$ converge to zero as $$n \to \infty$$ where s as a real number satisfies $$0  P: 1,060 I thought about the graph of that function and why the limit is "obvious" from the graph. Translating the graph picture into mathematics, I think an easy way is the mean value theorem. With it you find [tex] n^s-(n-1)^s=s(n+\xi)^{s-1}\to 0$$
 Quote by Gerenuk I thought about the graph of that function and why the limit is "obvious" from the graph. Translating the graph picture into mathematics, I think an easy way is the mean value theorem. With it you find $$n^s-(n-1)^s=s(n+\xi)^{s-1}\to 0$$