问题
解答题
求和12-22+32-42+…+992-1002.
答案
设S=12-22+32-42+…+992-1002.
则S=(1-2)(1+2)+(3-4)(3+4)+…+(99-100)(99+100)
=-3-7-11-…-199
=
×50(-3)+(-199) 2
=-5050
求和12-22+32-42+…+992-1002.
设S=12-22+32-42+…+992-1002.
则S=(1-2)(1+2)+(3-4)(3+4)+…+(99-100)(99+100)
=-3-7-11-…-199
=
×50(-3)+(-199) 2
=-5050