1乘以2分之1+2乘以3分之1+3乘以4分之1+4乘以5分之1+········+49乘以50分之1,等于多少?

题目

1乘以2分之1+2乘以3分之1+3乘以4分之1+4乘以5分之1+········+49乘以50分之1,等于多少?

答案

1/1*2+1/2*3+1/3*4+……+1/49*50
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/49-1/50)
=1-1/2+1/2-1/3+1/3-1/4+……+1/49-1/50
=1-1/50
=49/50