HMMT 二月 2000 · ADV 赛 · 第 3 题
HMMT February 2000 — ADV Round — Problem 3
题目详情
- Ev aluate . 2 n =1 n +2 n
解析
- W e kno w that = = . So, if w e sum this from 1 to 1 , all terms ex ept 2 n +2 n n ( n +2) 2 1 1 3 1 2 for + will an el out (a "teles oping" series). Therefore, the sum will b e . 2 2 4