# Math Help - n choose k proof

1. ## n choose k proof

Hi, I have to hand in my homework in two days and I have no idea how to prove the following (freely translated, English is not my native language so hope it makes sense):

"Show that for all positive whole numbers n and k, when n is bigger than or equal to k, the following applies:

(n
choose (k-1))+(n choose k)=((n+1) choose k)

My textbook uses the word choose, not sure if that's universal so "n choose k"=n!/k!(n-k)! so you know what I'm talking about.

Any help greatly appreciated!

2. Just calculate the sum directly. Get a common denominator using the recursion identity $j! = j (j - 1)!$. Everything falls out in two lines at the most.