Difference between revisions of "Hockey Stick Theorem"

Revision as of 22:07, 14 February 2014

Hockey Stick Theorem

The Hockey-stick theorem states: http://www.artofproblemsolving.com/Forum/code.php?hash=6bb7bab8c684ac4f4689a78c4994f8bad532c781&sid=07281467fd1a64b352d341e46a7f0f9a 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).

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-                                                                                                            '''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).
+The Hockey-stick theorem states:
+http://www.artofproblemsolving.com/Forum/code.php?hash=6bb7bab8c684ac4f4689a78c4994f8bad532c781&sid=07281467fd1a64b352d341e46a7f0f9a
+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).