Thread: Binomial expansion

Can anyone prove the binomial expansion:

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

Originally Posted by gtaplayr

Can anyone prove the binomial expansion:

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

this is certainly something that can be found all over the internet. see here

Originally Posted by gtaplayr

Can anyone prove the binomial expansion:

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

You only need to prove:

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

and this can be done reasonably easily by induction.

CB