HMMT 二月 1998 · 代数 · 第 3 题

HMMT February 1998 — Algebra — Problem 3

Find the sum of every even positive integer less than 233 not divisible by 10. r 2 ( 2 + 10 )

解析

Problem: Find the sum of every even positive integer less than 233 not divisible by 10. Solution: We find the sum of all positive even integers less than 233 and then subtract all the positive integers less than 233 that are divisible by 10. 2+4+ . . . +232 = 2(1+2+ . . . +116) = 116 · 117 = 13572. The sum of all positive integers less than 233 that are divisible by 10 is 10+20+ . . . +230 = 10(1+2+ . . . +23) = 2760. Then our answer is 13572-2760 = 10812 . √ √ 2( 2+ 10) r √