
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 (k1))+(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!(nk)! so you know what I'm talking about.
Any help greatly appreciated!

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