让一个乡村老教师寝食难安的数学题．

1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...1/(1+2+3+4+...+99)
=1/3+1/6+1/10+...1/4950
=2/(2*3)+2/(3*4)+2/(4*5)+…2/(99*100)
=(2/2-2/3)+(2/3-2/4)+(2/4-2/5)+...(2/99-2/100)
=2/2-2/100=49/50