Find the limit of each sequence that converges; if the sequence diverges, explain why.

(1) $\displaystyle z_n = (\frac{1+i}{\sqrt{3}})^n$

(2) $\displaystyle z_n = Log(1 + \frac{1}{n})$

Any help would be appreciated. Thanks!

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- Sep 10th 2008, 01:29 PMshadow_2145Complex Limits
Find the limit of each sequence that converges; if the sequence diverges, explain why.

(1) $\displaystyle z_n = (\frac{1+i}{\sqrt{3}})^n$

(2) $\displaystyle z_n = Log(1 + \frac{1}{n})$

Any help would be appreciated. Thanks! - Sep 10th 2008, 04:20 PMtopsquark
- Sep 10th 2008, 04:52 PM11rdc11
$\displaystyle z_n = Log(1 + \frac{1}{n})$

To see if it converges,

$\displaystyle \lim_{n \to \infty} Log\bigg(1 + \frac{1}{n}\bigg) = Log(1 + 0) = Log(1)$

$\displaystyle \lim_{n \to \infty}Log(1 + \frac{1}{n}) = 0$

so it converges to 0

Shot went to do something and came back and was too late