Question

1/2+1/3+2/3+1/4+2/4+3/4+……+58/60+59/60=?

Answer 1

先看

1/n+2/n+3/n+……+(n-1)/n

=(1+2+3+……+n-1)/n

=((n-1)(n-1+1)/2)/n

=(n-1)/2

则

1/2+1/3+2/3+1/4+2/4+3/4+……+58/60+59/60

=1/2+(3-1)/2+(4-1)/2+……+(60-1)/2

=(1+2+3+……+59)/2

=(59*(59+1)/2)/2

=885