Re: [問題] 請問這數列收斂至0還是1？

[isomorphism (山頭斜照卻相迎)]

※ 引述《age0925 (小立)》之銘言：
: as n→∞, (3/n)^(1/n)=?
: 謝謝解答

Ans:1 (Confirmed by TI89)

已知 lim 3^(1/n) as n→∞ = 3^0 = 1

再考慮 lim n^(1/n)

當 n=9999999999999  Then 9999999999999^(1/9999999999999) ~ 9999999999999^0

所以大膽地說: lim n^(1/n) = 1

Thus, lim (3/n)^(1/n) = lim 3^(1/n) / lim n^(1/n) = 1

這樣...應該沒錯吧......
所學不精~望各位不吝指正

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