The sum of the first 100 positive integers is 5,050. What is the sum of the firs

游客2025-02-27 7

问题 The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?

选项 A、10,100
B、10,200
C、15,050
D、20,050
E、20,100

答案 E

解析 The sum of the first n positive integers is given by

, so the sum of the first 200 positive integers is

=20,100.
Alternatively, letting

represent the sum of the first 100 positive integers, it is given that

= 5,050. Using this notation,

= 2(5,050)+ 10,000 = 10,100 + 10,000 = 20,100. The correct answer is E.

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