- #1

- 372

- 0

**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.

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]