2乘3分之1加3乘4加4乘5加.加49乘50分之1

题目

2乘3分之1加3乘4加4乘5加.加49乘50分之1

答案

1/2*3+1/3*4+1/4*5+……+1/49*50
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/49-1/50)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/49-1/50
=1/2-1/50
=24/50
=12/25