1/1×2=1/2=1-1/21/2×3=1/6=1/2-1/31/3×4=1/12=1/3-1/4.1/100×101=1/10001=1/100-1/1011/1×2+1/2×3+1/3×4+…+1/100×101=1-1/2+1/2-1/3+1/3-1/4+...++1/99-1/100+1/100-1/101=1+(-1/2+1/2)+(-1/3+1/3)-1/4+......