直接求和:-1²+2²-3²+4²-5²+6²-······-99²+100²

直接求和:-1²+2²-3²+4²-5²+6²-······-99²+100²
直接求和:-1²+2²-3²+4²-5²+6²-······-99²+100²

直接求和:-1²+2²-3²+4²-5²+6²-······-99²+100²
=(-1²+2²)+(-3²+4²)+(-5²+6²)-······(-99²+100²)
=(2+1)(2-1)+(4+3)+(4-3)+,+(100+99)+(100-99)
=1+2+3+4+...+99+100
=(1+100)+(2+99)+...+(50+51)
=101x50
=5050
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=(2^2-1^2)+(4^2-3^2)+...+(100^2-99^2)
=3+7+11+...+199
=(3+199)x50/2
=5050

5050

每2项合并，原式=(-1^2+2^2)+.....+(-99^2+100^2)=(-1+2)(1+2)+..+(-99+100)(99+100)=1+2+3+...+99+100=(1+100)*100/2=101*50=5050

-1²+2²-3²+4²-5²+6²-······-99²+100²
=(2²-1²)+(4²-3²)+(6²-5²)+······+(100²-99²)
=(2+1)×(2-1)+(4+3)×(4-3)+(6+5)×(6-5)+······+(100+99)×(100-99)
=(1+2)+(3+4)+(5+6)+·····+(99+100)