(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]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Sequences/series - just a silly question

**Physics Forums | Science Articles, Homework Help, Discussion**