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suppose this sequence:

[tex]

(-1)^{n} \sqrt{n} \left( \sqrt{n+1} - \sqrt{n} \right)

[/tex]

I tried to find the limit and got into this point:

[tex]

\lim \frac{n(-1)^{n}}{ \sqrt{n(n+1)} + n}

[/tex]

According to results, the limit doesn't exist. But how can I find it out? Can it be visible from the point I got to?

Thank you.

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# Why doesn't this have a limit?

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