1/n+2/n+……+(n-1)/n
=[1+2+……+(n-1)]/n
=[n(n-1)/2]/n
=(n-1)/2
所以
1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/40+2/40+...+39/40)
=(2-1)/2+(3-1)/2+……+(40-1)/2
=(1+2+……+39)/2
=[39*(39+1)/2]/2
=390