Question

1+1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/50+2/50+...+49/50)分数的简便

Answer 1

(1+2+...+(n-1))/n=[n(n-1)/2]/n=(n-1)/2

1+1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/50+2/50+...+49/50)

=1+1/2+2/2+...+49/2

=1+(1+2+3+...+49)/2

=1+49*50/2*1/2

=1+1225/2

=1227/2