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

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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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