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利用因式分解计算:(1-1/2²)(1-1/3²)···(1-1/9²)(1-1/10²)
人气:206 ℃ 时间:2020-03-24 19:26:56
解答
:(1-1/2²)(1-1/3²)···(1-1/9²)(1-1/10²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)·····(1-1/10)(1+1/10)
=1/2×3/2×2/3×4/3×···×9/10×11/10
=1/2×11/10
=11/20
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