The exam is behind, but I'll have to repeat it at least once :-)(adsbygoogle = window.adsbygoogle || []).push({});

Here are two problems I wasn't able to solve:

[tex]

\lim_{n \rightarrow \infty} n^2 \left[ \log \left( 1 + \frac{1}{n} \right) - \sin \left( \frac{1}{n} \right) \right]

[/tex]

I tried to solve it using Taylor, but it didn't help me...

And the second one, which I didn't even try, because I didn't catch it:

Convergence and absolute convergence of this:

[tex]

\sum_{n = 1}^{+\infty} (-1)^{n} \arctan \left( \sqrt{n^2 + 1} - \sqrt{n^2 - 1} \right)

[/tex]

How should I do that? IMO it would be sufficient that the arctan goes to 0 and then the sum would converge (Leibniz's rule)...

Thank you.

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# Homework Help: Problems from today calculus test

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