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Hockey-Stick Identity
## Formula
$$\sum_{r=k}^{n}{}^rC_k={}^{n+1}C_{k+1}$$
More generally:
$$\sum_{r=m}^{n}{}^rC_{r-m}={}^{n+1}C_{n-m+1}$$
## Usage
- Used for evaluating sums of binomial coefficients arranged along diagonals of Pascal's triangle.
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Hockey-Stick Identity
## Formula
$$\sum_{r=k}^{n}{}^rC_k={}^{n+1}C_{k+1}$$
More generally:
$$\sum_{r=m}^{n}{}^rC_{r-m}={}^{n+1}C_{n-m+1}$$
## Usage
- Used for evaluating sums of binomial coefficients arranged along diagonals of Pascal's triangle.
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