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(Diagonal sums)
The hockey stick identity: C(n,k) + C(n+1,k) + C(n+2,k) + ... + C(m,k) = C(m+1,k+1). It sums diagonals in Pascal's Triangle.
Example: C(2,2) + C(3,2) + C(4,2) = 1 + 3 + 6 = 10 = C(5,3). The diagonal forms a 'hockey stick' shape in the triangle.
This identity appears in probability and combinatorial proofs. It relates consecutive rows and simplifies summations.
