/sci/ - Science & Math

Is there any explanation for why the series
[math]1+x+x^2+x^3+...+x^\infty=\sum^\infty_{n=0}[/math] converges to [math]1\over{1-x}[/math] only for values [math]|x|<1[/math]? Or am I missing something really stupidly obvious?

Is it possible to only take labs? I need to make myself employable so I'm going to take hard labs in subjects I haven't even studied . Can I do this

>tfw theoretical computer science major
>math majors don't like me because CS and focus on the kinds of math a lot of the math majors seem to dislike or not be interested in
>CS major don't like me because math and they can't talk to me about anything

I'm so alone

>I chose this
>I chose to study this for 4 years and pit myself on an awful path
>I have one more grueling year +thesis to go

>I chose this