Difference between revisions of "2016 UNCO Math Contest II Problems/Problem 7"
(→Solution) |
(→Solution 2) |
||
| Line 8: | Line 8: | ||
==Solution 2== | ==Solution 2== | ||
| − | |||
| − | |||
This is a telescoping series: | 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 == | == See also == | ||
Revision as of 19:18, 4 March 2021
Contents
Problem
Evaluate
![\[S =\sum_{n=2}^{\infty} \frac{4n}{(n^2-1)^2}\]](http://latex.artofproblemsolving.com/5/8/f/58f783b714712db7d5b19d0f2b8d4de5d847cb83.png)
Solution
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 | ||
