SOLUTION: PLEASE HELP!!! Prove that U (n choose k-1) + (n choose k)=(n+1 choose k) for all natural numbers n and k, with k ≤ n.

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Question 1073142: PLEASE HELP!!!
Prove that U
(n choose k-1) + (n choose k)=(n+1 choose k)
for all natural numbers n and k, with k ≤ n.
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
is n choose k-1.
is n choose k.
The key to the proof is understanding that for any positive integer, ,
.
Let us add those two fractions.

Taking out the common factors, we get

Now we just have to deal with that simpler sum,
using as common denominator the product
.
So, we get
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