=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/99)(1+1/99)(1-1/100)(1+1/100)
=1/2 × 3/2×2/3 × 4/3×3/4 × 5/4×4/5 × ……× 100/99×99/100 ×101/100
=1/2×101/100
=101/200