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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)

Sorry, about the notation...

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...