# Math Help - Binomial expansion

1. ## Binomial expansion

Can anyone prove the binomial expansion:

$(x+y)^n$ = $\sum$ $\left(\begin{array}{c}n\\r\end{array}\right)$ $x^r.y^{n-r}$

2. Originally Posted by gtaplayr
Can anyone prove the binomial expansion:

$(x+y)^n$ = $\sum$ $\left(\begin{array}{c}n\\r\end{array}\right)$ $x^r.y^{n-r}$
this is certainly something that can be found all over the internet. see here

3. Originally Posted by gtaplayr
Can anyone prove the binomial expansion:

$(x+y)^n$ = $\sum$ $\left(\begin{array}{c}n\\r\end{array}\right)$ $x^r.y^{n-r}$
You only need to prove:

$(1+x)^n=\sum_{r=0}^n {n \choose r} x^r$

and this can be done reasonably easily by induction.

CB