Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 4"
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Latest revision as of 13:36, 24 November 2016
Problem
If is expanded and written in the form
where
and
are real numbers, then
![$\mathrm{(A) \ } -2^{50} \qquad \mathrm{(B) \ } 20^{50} - \frac{100!}{50!50!} \qquad \mathrm{(C) \ } \frac{100!}{(25!)^2 50!} \qquad \mathrm{(D) \ } 100! \left(-\frac 1{50!50!} + \frac 1{25!75!}\right) \qquad \mathrm{(E) \ } 0$](http://latex.artofproblemsolving.com/b/0/d/b0db8a534b52fc3ceda87a2da725848c4f801f32.png)
Solution
Notice that . We then have
.