1乘以3分之1加3乘以5分之1+5乘以7分之1+.49乘以51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+.49乘以51分之1

=1/2×(1-1/3)+1/2×(1/3-1/5)+……+1/2×(1/49-1/51)
=1/2×(1-1/3+1/3-1/5+……+1/49-1/51)
==1/2×(1-1/51)
=25/51