HMMT 二月 2004 · 冲刺赛 · 第 1 题
HMMT February 2004 — Guts Round — Problem 1
题目详情
- [5] Find the value of ( ) ( ) ( ) ( ) ( ) ( ) 6 6 6 6 6 6 1 2 3 4 5 6 2 + 2 + 2 + 2 + 2 + 2 . 1 2 3 4 5 6
解析
- Find the value of ( ) ( ) ( ) ( ) ( ) ( ) 6 6 6 6 6 6 1 2 3 4 5 6 2 + 2 + 2 + 2 + 2 + 2 . 1 2 3 4 5 6 Solution: 728 6 This sum is the binomial expansion of (1 + 2) , except that it is missing the first term, ( ) 6 0 6 2 = 1. So we get 3 − 1 = 728. 0