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  3. The sum of the first 50 positive integers is 1,275. What is the sum of the integ

The sum of the first 50 positive integers is 1,275. What is the sum of the integ

游客2025-02-24  40
问题 The sum of the first 50 positive integers is 1,275. What is the sum of the integers from 51 to 100, inclusive?
选项 A、2525
B、2550
C、325
D、3775
E、5050
答案 D
解析 前50个正整数的和是1275，问从51至100的整数(包括51和100)的和是多少?
解：本题的正确答案为(D)。为简化计算，考生可把从51到100之间的整数拆开来计算：51=50+1，52=50+2，…100=50+50，由此可得：51+52+…100=50×50+(1+2+…+50)=3775
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