# The Binomial Theorem

1. May 26, 2005

### Cincinnatus

It seems like this shouldn't be too difficult and yet i'm stumped.
I am trying to prove the binomial theorem.

(x+y)^n = the sum from k=0 to n of (x^k)*(y^n-k)*(The binomial coefficient n,k)

Anyway, I figure the best way to go about proving this is by induction.
It is easy to show that its true for n=1.
Then I assume that there exists an n_0 such that it is true for all n < n_0.
Now I want to show that the existence of this n_0 implies that the proposition is also true for n=n_0+1.

This is where I get stuck...
My question is, is this even the best way to go about proving this? If so, how can I finish the proof?

Maybe it would be better to give me a hint so I can figure it out on my own...

2. May 26, 2005

### Dr.Brain

http://planetmath.org/encyclopedia/InductiveProofOfBinomialTheorem.html [Broken]