(1-1/2) (1+1/2) (1-1/3) (1+1/3)...(1-1/100) (1+1/00) =(1-1/2) (1-1/3) ...(1-1/100) (1+1/2) (1+1/3)... (1+1/00) =1/2×2/3×……×99/100×3/2×4/3×……×101/100=1/100×101/2=101/200
