(101+103+…+199)-(90+92+…+188)=_.

问题描述:

(101+103+…+199)-(90+92+…+188)=______.

解法一:(101+103+…+199)-(90+92+…+188)
=(101+199)×[(199-101)÷2+1]÷2-(90+188)×[(188-90)÷2+1]÷2,
=300×50÷2-278×50÷2,
=(300-278)×25,
=22×25,
=550.
解法二:(101+103+…+199)-(90+92+…+188)
=(101-90)+(103-92)+…+(199-188)
=11×(

199−101
2
+1)
=11×50
=550
故答案为:550.