Question

1/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+...+(1/50+2/50

Answer 1

看一般的情形

1/n+2/n+3/n+.....+(n-1)/n=[n*(n-1)/2]/n=(n-1)/2

∴ 1/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+...+(1/50+2/50+3/50+...49/50)

=1/2 +2/2+3/2+4/2+......+50/2

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

=(1+50)*50/2

=51*25

=1275