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Difference between revisions of "2006 SMT/Advanced Topics Problems/Problem 3"

(Created page with "==Problem== Simplify: <math> \sum_{k=10}^{2006}\binom{k}{10} </math> (Your answer should contain no summations but may still contain binomial coefficients/combinations). ==Solut...")
 
(No difference)

Latest revision as of 20:20, 27 May 2012

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 $\sum_{k=10}^{2006}\binom{k}{10}=\boxed{\binom{2007}{11}}$.

See Also

2006 SMT/Advanced Topics Problems

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