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The sum of the first 100 positive integers is 5,050. What is the sum of the firs
The sum of the first 100 positive integers is 5,050. What is the sum of the firs
游客
2025-02-27
24
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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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