(1除以1乘2)+(1除以2乘3)+(1除以3乘4)+……(1除以48乘49)+(1除以49乘50

问题描述:

(1除以1乘2)+(1除以2乘3)+(1除以3乘4)+……(1除以48乘49)+(1除以49乘50

1/[n*(n+1)]=1/n-1/(n+1),n=1,2,3......
所以原式=1/1-1/2+1/2-1/3+1/3-1/4+...+1/48-1/49+1/49-1/50
=1-1/50
=49/50

无解

1除以1乘2)+(1除以2乘3)+(1除以3乘4)+……(1除以48乘49)+(1除以49乘50
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/49-1/50
=1/1-1/50
=1-1/50
=49/50

原式=1/1-1/2+1/2-1/3+1/3-1/4+...+1/48-1/49+1/49-1/50
=1-1/50
=49/50