1/1×3+1/3×5+1/5×7+…+1/99×101=(1/2)*(1/1-1/3)+(1/2)*(1/3-1/5)+(1/2)*(1/5-1/7)+…+(1/2)*(1/99-1/101)=(1/2)*(1/1-1/3+1/3-1/5+1/5-1/7+…+1/99-1/101)=(1/2)*(1-1/101)=50/101