HMMT 二月 2001 · 冲刺赛 · 第 14 题
HMMT February 2001 — Guts Round — Problem 14
题目详情
- [8] Find the exact value of 1 + . 2 1+ 1 1+ 2 1+ 1+ ···
解析
- [8] Find the exact value of 1 + . 2 1+ 1 1+ 2 1+ 1+ ··· 1 1 Solution: Let x be what we are trying to find. x − 1 = ⇒ − 1 = 2 x − 1 1+ 1 1+ 2 1+ 1+ ··· √ 2 2 2 ⇒ = x ⇒ x − 2 = 0, so x = 2 since x > 0. 1 1 1+ − 1 2 x − 1 1+ 1+ ···