(adsbygoogle = window.adsbygoogle || []).push({}); sequences/series - just a silly question :)

I think the limits I have found for the sequences below are right, but I'm not sure on how to approach the series. Please, help me understand what I should do to find the series when a sine, cosine, or a ln appears in the formula. Is there a general procedure?

Thank you very much.

1.

[tex] \lim _{n \to \infty} \frac{1}{n} = 0 [/tex]

[tex] \lim _{n \to \infty} \sin \left( \frac{1}{n} \right) = \sin 0 = 0 [/tex]

[tex] \sum _{n = 1} ^{\infty} \sin \left( \frac{1}{n} \right) = ? [/tex]

2.

[tex] \lim _{n \to \infty} \frac{n}{n+1} = \lim _{n \to \infty} \frac{1}{1+\frac{1}{n}}=1 [/tex]

[tex] \lim _{n \to \infty} \ln \left( \frac{n}{n+1} \right) = \ln 1 = 0 [/tex]

[tex] \sum _{n = 1} ^{\infty} \ln \left( \frac{n}{n+1} \right) = ? [/tex]

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# Sequences/series - just a silly question

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