1/2*4+1/4*6+1/6*8+1/8*10+---+1/198*200

问题描述:

1/2*4+1/4*6+1/6*8+1/8*10+---+1/198*200

每一项都裂项即
1/2*4=(1/2-1/4)/2
1/4*6=(1/4-1/6)/2
.
则原式=(1/2-1/4+1/4-1/6+1/6-1/8+……+1/198-1/200)/2
=(1/2-1/200)/2
=99/400