Christmas Stocking Theorem
The Christmas stocking theorem, also known as the hockey stick theorem, states that the sum of a diagonal string of numbers in Pascal's
triangle starting at the 
th entry from the
top (where the apex has 
) on left edge
and continuing down 
rows is equal to
the number to the left and below (the "toe") bottom of the diagonal (the
"heel"; Butterworth 2002). This follows from the identity
 |
where 
is a binomial
coefficient.
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Abel's binomial theorem
