867 views

### Proving $(x+y)^n = \sum\limits_{k=0}^n \binom{n}{k} x^k y^{n-k}$ [duplicate]

I'm reading Serge Lang's 'Analysis I', and there's a problem I cannot figure out how to prove: Problem: Prove by induction that (x+y)^n = \sum_{k=0}^n \begin{pmatrix} n \\ k \end{pmatrix} x^k y^{...
I'm trying to prove the Binomial Theorem using induction. I know that I am supposed to use ${n\choose k} + {n\choose k - 1} = {n + 1 \choose k}$. I just really want to know how to use this equation ...