1/（1+2）+1/(2+3)+1/(3+4)+```````+1/(99+100)=1/(1+2)+1/2-1/3+1/3-1/4+1/4-1/5+```````+1/99-1/100=1/(1+2)+1/2-1/100=1/3+1/2-1/100=5/6-1/100=247/300
1+2+3+4+5+6+...+99=4950
