How to find the limit of series? (What should I know?) There is a couple of limits that I failed to find:
$$\lim_{n\to\infty}\frac 1 2 + \frac 1 4 + \frac 1 {8} + \cdots + \frac {1}{2^{n}}$$
and
$$\lim_{n\to\infty}1 - \frac 1 3 + \frac 1 9 - \frac 1 {27} + \cdots + \frac {(-1)^{n-1}}{3^{n-1}}$$
There is no problem to calculate a limit using Wolfram Alfa or something like that. But what I am interested in is the method, not just a concrete result.
So my questions are:


*

*What should I do when I need a limit of infinite sum? (are there any rules of thumb?)

*What theorems or topics from calculus should I know to solve these problems better?


I am new to math and will appreciate any help. Thank you!

They are sums of geometric progressions. 
The first it's
$$\frac{\frac{1}{2}}{1-\frac{1}{2}}=1.$$
The second it's $$\frac{1}{1+\frac{1}{3}}=\frac{3}{4}.$$
