1/(1*3)+1/(2*4)+1/(3*5)一直到+1/(99*101)

1/(1*3)+1/(2*4)+1/(3*5)+……+1/(99*101) =[2/(1*3)+2/(2*4)+2/(3*5)+……+2/(99*101)]/2 =[(1/1-1/3)+(1/2-1/4)+(1/3-1/5)+……+(1/98-1/100)+(1/99-1/101)]/2 =(1+1/2-1/100-1/