1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15+1/15*17+1/17*19+1/19*21=

问题描述:

1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15+1/15*17+1/17*19+1/19*21=

原式=(1-1/3)×1/2+(1/3-1/5)×1/2+(1/5-1/7)×1/2……
+(1/19-1/21)×1/2
=(1-1/3+1/3-1/5+1/5-……+1/19-1/21)×1/2
=(1-1/21)×1/2
=10/21
100对!