Let \[p,q\in \mathbb{N}\]
such that
\[\frac{p}{q}=1-\frac{1}{2}+\frac{1}{3}-....-\frac{1}{1318}+\frac{1}{1319}\]
Prove that \[1979\] divides $p$.
IMO 1979
Re: IMO 1979
Well,my solution should be this...
we will use the Catalan identity:
$1-\frac{1}{2}+\frac{1}{3}-......-\frac{1}{2n}=\frac{1}{n+1}+\frac{1}{n+2}+.....+\frac{1}{2n}$
This will yield the result.
we will use the Catalan identity:
$1-\frac{1}{2}+\frac{1}{3}-......-\frac{1}{2n}=\frac{1}{n+1}+\frac{1}{n+2}+.....+\frac{1}{2n}$
This will yield the result.
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