Question

用适当的方法化简计算：(1-2²/1)(1-3²/1)(1-4²/1)...（1-99²/1）（1-100²/1）

Answer 1

用适当的方法化简计算：
(1-2²/1)(1-3²/1)(1-4²/1)...（1-99²/1）（1-100²/1）
=(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)
=2/3x3/4x4/5x……x99/100x100/101x2/1x3/2x4/3x……x100/99
=2/101x100/1
=200/101
=0.505

Answer 2

=(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