2005/1*3+2005/3*5+2005/5*7+···2005/99*101=2005/[1/(1*3)+1/(3*5)+1/(5*7)+.+1/(99*101)]=2005/[(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+.+(1/99-1/101)/2]=2005/{[(1-1/3)+(1/3-1/5)+(1/5-1/7)+.+(1/99-1/101)]/2}=2005/{[1+(-1/3+1/3)+(-1/5+1/5)+(-1/7+.+1/99)-1/101]/2}=2005/{[1-1/101]/2}=2005/{[100/101]/2}=2005/{50/101}=2005*{101/50}=4050.1