原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/100)(1+1/100)=1/2*3/2*2/3*4/3*...*99/100*101/100=1/2*(3/2*2/3)*(4/3*3/4)*...(100/99*99/100)*101/100=1/2*101/100=101/200