计算:(2²+4²+……+100²)-(1²+3²+……+99²)

问题描述:

计算:(2²+4²+……+100²)-(1²+3²+……+99²)

(2²+4²+……+100²)-(1²+3²+……+99²)
=(2²-1²)+(4²-3²)+(6²-5²)+……+(100²-99²)
=(1+2)+(3+4)+(5+6)+……+(99+100)
=(1+100)*100/2
=5050

(2²+4²+……+100²)-(1²+3²+……+99²)=(2²-1²)+(4²-3²)+(6²-5²)+……+(100²-99²)=(1+2)+(3+4)+(5+6)+……+(99+100)=5050