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1989 AHSME Problems/Problem 29

Revision as of 15:47, 31 August 2008 by 1=2 (talk | contribs) (New page: ==Problem== What is the value of the sum <math>S=\sum_{k=0}^{49}(-1)^k\binom{99}{2k}=\binom{99}{0}-\binom{99}{2}+\binom{99}{4}-\cdots -\binom{99}{98}</math>? ==Solution== {{solution}} ==...)
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Problem

What is the value of the sum $S=\sum_{k=0}^{49}(-1)^k\binom{99}{2k}=\binom{99}{0}-\binom{99}{2}+\binom{99}{4}-\cdots -\binom{99}{98}$?

Solution

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See also

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