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Limit

Alexmahone

Active member
Jan 26, 2012
268
Find $\displaystyle\lim_{n\to\infty}\frac{\sqrt[n]{n}}{\sqrt[n+1]{n+1}}$.
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,493
$\sqrt[n]{n}=e^{\frac{\ln n}{n}}$ and $\frac{\ln n}{n}\to 0$ as $n\to\infty$.
 

Alexmahone

Active member
Jan 26, 2012
268

Plato

Well-known member
MHB Math Helper
Jan 27, 2012
196
Find $\displaystyle\lim_{n\to\infty}\frac{\sqrt[n]{n}}{\sqrt[n+1]{n+1}}$.
Do you know this limit
$\displaystyle\lim _{u \to \infty } \sqrt{u}=~?$
 

Alexmahone

Active member
Jan 26, 2012
268

Plato

Well-known member
MHB Math Helper
Jan 27, 2012
196

Alexmahone

Active member
Jan 26, 2012
268

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,493
I agree.