(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(here (n,k) reads n choose k)(and again, please excuse that i don't use latex)

claim: (n,0) + (n,1) + (n,2) + ... (n,n) = 2^{n}

2. Relevant equations

binomial theorem

3. The attempt at a solution

proof: sum(k=0 to n of (n,k)) = sum(k=0 to n of (n,k))*1^{k}*1^{n-k}.

by the binomial theorem, (x + y)^{n}= sum(k=0 to n of (n,k))*x^{k}y^{n-k}, so letting x, y = 1, then (1 + 1)^{n}= 2^{n}= sum(k=0 to n of (n,k))*1^{k}*1^{n-k}= sum(k=0 to n of (n,k)).

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Please check my proof of sum of n choose k = 2^n

**Physics Forums | Science Articles, Homework Help, Discussion**