How can we prove that [tex]n^s-(n-1)^s[/tex] converge to zero as [tex]n \to \infty[/tex] where s as a real number satisfies [tex]0<s<1[/tex]?(adsbygoogle = window.adsbygoogle || []).push({});

I am specifically looking for a more or less elementary proof for this for real s. I think we can use the infinite binomial expansion, but I am looking for something that does not require more than elementary calculus.

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# Proof of convergence

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