Question

1/1x2+1/2x3+1/3x4+...+1/19x20 请说出道理

Answer 1

1/[n(n+1)]=1/n-1/(n+1)

1/1x2+1/2x3+1/3x4+...+1/19x20

=1-1/2+1/2-1/3+1/3+1/4+...+1/19-1/20

=1-1/20=19/20