Question

利用因式分解计算：（1-1/2²）（1-1/3²•……•（1-1/100²） 急用!

Answer 1

平方差
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/100)(1+1/100)
=1/2×3/2×2/3×4/3×3/4×5/4.×99/100×101/100 前后抵消
=1/2×101/100
=101/200
=0.505