Prove that for every integer $n$ ($n > 1$) there exist two positive integers $x$ and $y$ ($x \leq y$) such that $$\frac{1}{n} = \frac{1}{x(x+1)} + \frac{1}{(x+1)(x+2)} + \cdots + \frac{1}{y(y+1)}$$
Source:
Tags: algebra, equation, egyptian fractions
Prove that for every integer $n$ ($n > 1$) there exist two positive integers $x$ and $y$ ($x \leq y$) such that $$\frac{1}{n} = \frac{1}{x(x+1)} + \frac{1}{(x+1)(x+2)} + \cdots + \frac{1}{y(y+1)}$$