Hockey Stick Theorem

                                                                                                           Hockey-stick theorem

The Hockey-stick theorem states: {n \choose 0}+{n+1 \choose 1}+\cdots+{n+k \choose k} = {n+k+1 \choose k}. Its name is due to the "hockey-stick" which appears when the numbers are plotted on Pascal's Triangle, as shown in the representation of the theorem to the right (where n=2 and k=3).