Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 14, 2011"
m (Simplified answer, and boxed it.) |
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At this point, all that is left is arithmetic. | At this point, all that is left is arithmetic. | ||
The expression equals <math>\frac{(42!)^2*2*24}{41!*43!*6^2}=\frac{42!}{41!}*\frac{42!}{43!}*\frac{48}{36}=42*\frac{1}{43}*\frac{4}{3}</math>. | The expression equals <math>\frac{(42!)^2*2*24}{41!*43!*6^2}=\frac{42!}{41!}*\frac{42!}{43!}*\frac{48}{36}=42*\frac{1}{43}*\frac{4}{3}</math>. | ||
− | This trivially simplifies to <math>\frac{168}{129}</math>. | + | This trivially simplifies to <math>\frac{168}{129}=\boxed{\frac{56}{43}}</math>. |
Latest revision as of 11:58, 20 June 2012
Problem
AoPSWiki:Problem of the Day/July 14, 2011
Solution
We begin by factoring the given expression, , to . Then, writing this as multiple products and shifting the indices for clarity, we get . Clearly, this equals . At this point, all that is left is arithmetic. The expression equals . This trivially simplifies to .