2006 SMT/Advanced Topics Problems/Problem 3

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Problem

Simplify: $\sum_{k=10}^{2006}\binom{k}{10}$ (Your answer should contain no summations but may still contain binomial coefficients/combinations).

Solution

Recall from the Hockey Stick Identity that $\sum_{i=n}^{j}\binom{i}{n}=\binom{j+1}{n+1}$ . Therefore, we have $\sum_{k=10}^{2006}\binom{k}{10}=\boxed{\binom{2007}{11}}$ .

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2006 SMT/Advanced Topics Problems/Problem 3

Problem

Solution

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