逆用平方差公式计算:(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/10²)
问题描述:
逆用平方差公式计算:(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/10²)
答
(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/10²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/10)(1-1/10)
=(1+1/2)(1+1/3)(1+1/4)..(1+1/10)(1-1/2)(1-1/3)(1-1/4)...(1-1/10)
=3/2×4/3×5/4×...×11/10×1/2×2/3×3/4×...×9/10
=11/2×1/10
=11/20