1乘以3分之1加3乘以5分之1+5乘以7分之1+.19乘以21分之1

问题描述:

1乘以3分之1加3乘以5分之1+5乘以7分之1+.19乘以21分之1

1/1*3+1/3*5+1/5*7+...+1/19*21
=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/19-1/21)
=1/2(1-1/21)
=1/2*20/21
=10/21