## Unit Fractions

A unit fraction is a fraction with denominator equal to 1. Every unit fraction can be written as the sum as two other unit fractions.
For example
$\frac{1}{2}=\frac{1}{3}+ \frac{1}{6}$

The proof is quire simple.
Take unit fraction
$\frac{1}{n}$
.
\begin{aligned} \frac{1}{n+1} + \frac{1}{n(n+1)} &= \frac{n}{n(n+1)} + \frac{1}{n(n+1)} \\ &= \frac{n+1}{n(n+1)} \\ &= \frac{1}{n}\end{aligned}