Linked Questions

4
votes
4answers
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^{...
1
vote
0answers
25 views

Prove the Binomial Expansion with Induction [duplicate]

I'm having trouble with proving the binomial expansion with the principle of mathematical induction. I don't really know where to start, but I think that I managed to prove the first step. The ...
1
vote
1answer
941 views

Prove the Binomial Theorem using Induction

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 ...