2016 UNCO Math Contest II Problems/Problem 7
Revision as of 10:57, 23 October 2023 by Namelyorange (talk | contribs)
Contents
[hide]Problem
Evaluate
Solution
First, we perform fractional decomposition on the summed expression. Let . Multiplying both sides by and expanding gives Therefore, we have the system of equations . Adding the two equations gives , while subtracting the two gives .
Therefore, , so
Writing out the first few terms and rearranging, we have , which telescopes to
Solution 2
This is a telescoping series:
(1−1/9)+(1/4−1/16)+(1/9−1/25)+(1/16−1/36)+(1/25−1/49)+...=5/4
See also
2016 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |