Hockey-stick identity
In combinatorics, the hockey-stick identity, Christmas stocking identity, boomerang identity, Fermat's identity or Chu's Theorem, states that if n ≥ r ≥ 0 {\displaystyle n\geq r\geq 0} are integers, then ( r r ) + ( r + 1 r ) + ( r + 2 r ) + ⋯ + ( n r ) = ( n + 1 r + 1 ) . {\displaystyle {\binom {r}{r}}+{\binom {r+1}{r}}+{\binom {r+2}{r}}+\cdots +{\binom {n}{r}}={\binom {n+1}{r+1}}.} The name stems from the graphical representation of the identity on Pascal's triangle: when the addends represented in the summation and the sum itself are highlighted, the shape revealed is vaguely reminiscent of those objects (see hockey stick, Christmas stocking).