## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

Proof

We will use the induction principle. Fix arbitrary $a\text{,}b\in \mathbb{R}$ and let the preceding equality be the assertion $P\left(n\right)$. Then $P\left(1\right)$ is obviously true. Assume that $P\left(n\right)$ is true for some $n$. Then by Lemma 2.11,

$\begin{array}{cc}\hfill {\left(a+b\right)}^{n+1}=& \left(a+b\right)\sum _{k=0}^{n}\frac{n!}{k!\left(n-k\right)!}{a}^{n-k}{b}^{k}\hfill \\ \hfill =& \sum _{k=0}^{n}\frac{n!}{k}\hfill \end{array}$

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required