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#### Alexmahone

##### Active member

- Jan 26, 2012

- 268

Find $\displaystyle\lim_{n\to\infty}\frac{\sqrt[n]{n}}{\sqrt[n+1]{n+1}}$.

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- Thread starter
- #1

- Jan 26, 2012

- 268

Find $\displaystyle\lim_{n\to\infty}\frac{\sqrt[n]{n}}{\sqrt[n+1]{n+1}}$.

- Jan 30, 2012

- 2,525

$\sqrt[n]{n}=e^{\frac{\ln n}{n}}$ and $\frac{\ln n}{n}\to 0$ as $n\to\infty$.

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- #3

- Jan 26, 2012

- 268

So are you saying that the answer is $\displaystyle\frac{1}{1}=1$?$\sqrt[n]{n}=e^{\frac{\ln n}{n}}$ and $\frac{\ln n}{n}\to 0$ as $n\to\infty$.

Do you know this limitFind $\displaystyle\lim_{n\to\infty}\frac{\sqrt[n]{n}}{\sqrt[n+1]{n+1}}$.

$\displaystyle\lim _{u \to \infty } \sqrt

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- #5

- Jan 26, 2012

- 268

Do you know this limit

$\displaystyle\lim _{u \to \infty } \sqrt{u}=~?$

It's 1.

What is the answer to the OP?It's 1.

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- #7

- Jan 26, 2012

- 268

$\displaystyle\frac{1}{1}=1$What is the answer to the OP?

- Jan 30, 2012

- 2,525

I agree.