HMMT 二月 1998 · CALC 赛 · 第 9 题
HMMT February 1998 — CALC Round — Problem 9
题目详情
英文原题
Question Nine . [7 points]
∞
Evaluate 1
∑
n − 1
n ⋅ 2
n = 1
解析
英文解析
- Problem: Evaluate .
n − 1
n · 2
n =1
x 2
Solution: Note that if we take the integral of f ( x ) in problem 4, we get the function F ( x ) = x + +
2 · 2
x 1 13 + . . . . Evaluating this integral in the interval [0 , 1], we get 1 + + + . . . , which is the desired sum.
2 2
3 · 2 2 · 2 3 · 2
∫
Hence dx = 2 ln 2.21
2 − xy 20 x