University of South Carolina High School Math Contest/1993 Exam/Problem 30
Problem
![$\frac 1{1\cdot 2\cdot 3\cdot 4} + \frac 1{2\cdot 3\cdot 4\cdot 5} + \frac 1{3\cdot 4\cdot 5\cdot 6} + \cdots + \frac 1{28\cdot 29\cdot 30\cdot 31} =$](http://latex.artofproblemsolving.com/b/f/1/bf1929d3d66cb74d3d7de3d191c627f840e2e93b.png)
![$\mathrm{(A) \ }1/18 \qquad \mathrm{(B) \ }1/21 \qquad \mathrm{(C) \ }4/93 \qquad \mathrm{(D) \ }128/2505 \qquad \mathrm{(E) \ } 749/13485$](http://latex.artofproblemsolving.com/2/c/f/2cf3f0266f99e6debc69b0abdc9bdbe1e0b394f2.png)
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Factoring out a telescopes the sum to
.
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Factoring out a telescopes the sum to
.
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