Discrete random variable with $f(x)=c(2x-1)$ I feel really stupid because I don't understand this example at the start of my textbook. The chapter is discrete random variables and it starts out with this example with no explanation. I understand the rule that $\sum f(x)=1$ so I can see why there is a $1$ at the front of this equation. I don't understand how the equation went from $\sum (2x-1)$ to $2\sum x-12$. And the step after that - are they following a formula there? I'm having trouble finding information on the internet that explains this type of problem. Thank you in advance.
$$f(x)=c(2x-1) \text{ for } x=1,2,\dots,12$$
$$1=c\sum_{x=1}^{12} (2x-1)=c\left[2\sum_{x=1}^{12} x-12\right]=c\left[\frac{2(12)(13)}{2}-12\right]=c(12)^2$$

Thanks, I found the rules:
$ \displaystyle{ \sum_{i=1}^{n} c  } = cn$
$ \displaystyle{ \sum_{i=1}^{n} i 
= { n(n+1) \over 2 } } $ 
So, $\displaystyle c\sum_{x=1}^{12} (2x-1)=c[2\sum_{x=1}^{12} x-\sum_{x=1}^{12}1]=c[2\sum_{x=1}^{12} x-(1)(12)]$
(by the first rule)
And the rest is easy following the second rule.
