利用因式分解计算:(1-1/2²)(1-1/3²)(1-1/4²)···(1-/n²)
人气:269 ℃ 时间:2020-03-29 19:47:48
解答
:(1-1/2²)(1-1/3²)(1-1/4²)···(1-/n²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)·····(1-1/n)(1+1/n)
=1/2×3/2×2/3×4/3×3/4×5/4×···×(n-1)/n×(n+1)/n
=1/2×(n+1)/n
=(n+1)/(2n)
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