![SOLVED: 27. Prove the hockeystick identity +6) = (n+r+ 1) k k=0 whenever n and r are positive integers, a) using combinatorial argument: b) using Pascal'identity: SOLVED: 27. Prove the hockeystick identity +6) = (n+r+ 1) k k=0 whenever n and r are positive integers, a) using combinatorial argument: b) using Pascal'identity:](https://cdn.numerade.com/ask_images/acfc373e984644c481a2a0727f9aebd5.jpg)
SOLVED: 27. Prove the hockeystick identity +6) = (n+r+ 1) k k=0 whenever n and r are positive integers, a) using combinatorial argument: b) using Pascal'identity:
![combinatorics - Proof of the hockey stick/Zhu Shijie identity $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$ - Mathematics Stack Exchange combinatorics - Proof of the hockey stick/Zhu Shijie identity $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$ - Mathematics Stack Exchange](https://i.stack.imgur.com/7tW63.jpg)
combinatorics - Proof of the hockey stick/Zhu Shijie identity $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$ - Mathematics Stack Exchange
![SOLVED: COSICr the s0-called hOckey-StICk Identity: 2()-(+i) Fove cie hockV- stick iclemily; either induetively comhinatorially. For (e iuductive proof, use Pascal identity: (+) + for the combinatorial proof, considler forming COHittce 0l size ! + [ SOLVED: COSICr the s0-called hOckey-StICk Identity: 2()-(+i) Fove cie hockV- stick iclemily; either induetively comhinatorially. For (e iuductive proof, use Pascal identity: (+) + for the combinatorial proof, considler forming COHittce 0l size ! + [](https://cdn.numerade.com/ask_images/9e704956784c4d4ab550338b4f55c0e8.jpg)
SOLVED: COSICr the s0-called hOckey-StICk Identity: 2()-(+i) Fove cie hockV- stick iclemily; either induetively comhinatorially. For (e iuductive proof, use Pascal identity: (+) + for the combinatorial proof, considler forming COHittce 0l size ! + [
![MathType på Twitter: "This identity is known as the Hockey-stick Identity or the Christmas Sock Identity in reference to its graphical representation on Pascal's triangle #Combinatorics #MathType https://t.co/Ogv0Zbnjac" / Twitter MathType på Twitter: "This identity is known as the Hockey-stick Identity or the Christmas Sock Identity in reference to its graphical representation on Pascal's triangle #Combinatorics #MathType https://t.co/Ogv0Zbnjac" / Twitter](https://pbs.twimg.com/media/ECvfDqAX4AEZSGx.jpg)