Quote:
Originally Posted by great_math  ![\ 1,\sqrt{2},\sqrt[3]{3}.....,\sqrt[n]{n}](http://www.mathhelpforum.com/math-help/latex2/img/0685d03184ac3ce73629c87154532109-1.gif "\ 1,\sqrt{2},\sqrt[3]{3}.....,\sqrt[n]{n}")
Determine the largest number in the above sequence | The function  has a maximum turning point at x = e. Since 2 < e < 3, the question now becomes a simpler one:
"Which is bigger,  or ![\sqrt[3]{3}](http://www.mathhelpforum.com/math-help/latex2/img/00183145853114fdd8d947a663084fb6-1.gif "\sqrt[3]{3}") " .... Which is more or less the same as asking "Which is bigger,  or ![(\sqrt[3]{3})^6](http://www.mathhelpforum.com/math-help/latex2/img/79a4e1eaeb2250548842e88b4d621e81-1.gif "(\sqrt[3]{3})^6") " ....
Alternatively, note that has the same value as ![\sqrt[4]{4} = 4^{1/4}](http://www.mathhelpforum.com/math-help/latex2/img/57e379f25267e2cf6a81a98db02296f9-1.gif "\sqrt[4]{4} = 4^{1/4}") .....
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Determine largest number: 
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