Sean $a$ y $b$ números arbitrarios y sea $n\in \mathbb{N}$. Demuestra que:

$$(a+b{)}^n=(\genfrac{}{}{0ex}{}{n}{0})a^n+(\genfrac{}{}{0ex}{}{n}{1})a^{n-1}{b}^1+\cdots +(\genfrac{}{}{0ex}{}{n}{r})a^{n-r}{b}^r+\cdots +(\genfrac{}{}{0ex}{}{n}{n-1})a^1{b}^{n-1}+(\genfrac{}{}{0ex}{}{n}{n})b^n$$