Difference between revisions of "2000 SMT/Advanced Topics Problems/Problem 3"
(Created page with "==Problem== Evaluate <math>\sum^{\infty}_{n=1}\frac{1}{n^2+2n}.</math> ==SMT Solution== We know that <math>\frac{1}{n^2+2n}=\frac{1}{n(n+2)}=\frac{\frac{1}{n}-\frac{1}{n+...") |
(No difference)
|
Latest revision as of 09:27, 24 July 2020
Problem
Evaluate
SMT Solution
We know that So, if we sum this from to all terms except for will cancel out (a "telescoping" series). Therefore, the sum will be
Credit
Problem and solution were taken from https://sumo.stanford.edu/old/smt/2000/