# Binomial expansion

• July 31st 2009, 04:30 PM
gtaplayr
Binomial expansion
Can anyone prove the binomial expansion:

$(x+y)^n$ = $\sum$ $\left(\begin{array}{c}n\\r\end{array}\right)$ $x^r.y^{n-r}$
• July 31st 2009, 04:52 PM
Jhevon
Quote:

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
• August 1st 2009, 12:01 AM
CaptainBlack
Quote:

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