推 aacvbn:感恩感恩^^ 220.139.244.9 08/06
※ 引述《aacvbn (Combat，喝了在上)》之銘言：
: lim (1-x^1/2)(1-x^1/3)(1-x^1/4)‧‧‧(1-x^1/n)
: ----------------------------------------
: x→1 (1-x)^n-1
: 求詳解
: 感恩(*^^*)
用配的
{(1-x^(1/2)/(1-x)}...{(1-x^(1/n)/(1-x)}
每個分母的1-x須與其分子化約
代入次方差公式:
1-x= [1-x^(1/2)][1+x^(1/2)]
1-x=[1-x^(1/3)][1+x^(1/3)+x^(2/3)]
1-x={1-x^(1/4)][1+x^(1/4)+x^(2/4)+x^(3/4)]
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Ans:1/n!
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