OG12 PS157

littlecynthia

For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?
A 10,100
B 20,200
C 22,650
D 40,200
E 45,150

坚定之路

150(150+1)/2-49(49+1)/2=75*151-49*25=20,200

littlecynthia

为啥这样算呢?

150(150+1)/2-49(49+1)/2=75*151-49*25=20,200

-- by 会员 坚定之路 (2010/9/3 14:58:28)

坚定之路

99前面有49个偶数，301前面有150个偶数，所以99至301之间的偶数之和等于前150个偶数之和减去前49个偶数之和。