推 terry1122:非常感謝!!! 59.104.225.208 02/17
※ 引述《terry1122 (我會一直守候著你)》之銘言：
: lim {(x)^1/2-1}*{(x)^1/4-1}*{(x)^1/6-1}
: x->1 ---------------------------------------
: {(x)^1/3-1}*{(x)^1/5-1}*{(x)^1/7-1}
lim {(x)^1/2-1}*{(x)^1/4-1}*{(x)^1/6-1}
x->1 ---------------------------------------
{(x)^1/3-1}*{(x)^1/5-1}*{(x)^1/7-1}
(x)^1/2-1 (x)^1/4-1 (x)^1/6-1
= lim ----------- * lim ----------- * lim -----------
x->1 (x)^1/3-1 x->1 (x)^1/5-1 x->1 (x)^1/7-1
接下來用羅必達一個個算出來就可以了
1
---------
2(x)^1/2
= lim ----------- * ......
x->1 1
---------
3(x)^2/3
3 5 7
= --- * --- * ---
2 4 6
: lim {1-(x)^1/2}*{1-(x)^1/3}*{1-(x)^1/4}*.....*{1-(x)^1/n}
: x->1 -------------------------------------------------------
: (1-x)^(n-1)
lim {1-(x)^1/2}*{1-(x)^1/3}*{1-(x)^1/4}*.....*{1-(x)^1/n}
x->1 -------------------------------------------------------
(1-x)^(n-1)
1-(x)^1/2 1-(x)^1/3
= lim ------------- * lim ------------- * ...
x->1 1 - x x->1 1 - x
1 1 1
= --- * --- * ... = -----
2 3 n!
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