# Prove that <munder> <mo movablelimits="true" form="prefix">lim <mrow class="MJX-TeXAtom-

Prove that
$\underset{n\to +\mathrm{\infty }}{lim}\left(\frac{1}{n}-\frac{1}{n+1}\right)=0$
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Valeria Wolfe
you have
$\frac{1}{n}-\frac{1}{n+1}=\frac{1}{n\left(n+1\right)}$
and
$0\le \frac{1}{n\left(n+1\right)}\le \frac{1}{{n}^{2}}$
then because
$\underset{n\to +\mathrm{\infty }}{lim}\frac{1}{{n}^{2}}=0$
we have $\underset{n\to +\mathrm{\infty }}{lim}\left(\frac{1}{n}-\frac{1}{n+1}\right)=0$