Hockey stick identity

 


The picture above shows Pascal's triangle from row 0 to row 7.
The red number 35 is 7C3.
Green numbers add up to this.
Green number sum = 6C2 + 5C2 + 4C2 + 3C2 + 2C2

This is an example of hockey stick identity.

Another example:
2C2 + 3C2 + ...  10C2 = 11C3

Formally:






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