My urn contains 3 red, 2 green and 1 white ball. I pick a ball with replacement until I pick the second color. 

What is the average number of picks for picking the second color?

With the expected value formula I got the following.

$EX=\sum\limits_{k=2}^\infty k[\frac{1}{2}r^{k-1}+\frac{2}{3}g^{k-1}+\frac{5}{6}w^{k-1}]$

Where r, g and w are the probabilites of drawing a red, green, or white ball.

I don't know how to calculate this sum, and I am not sure this is the right way to solve this excercise.


Question: Layman's guide to getting started with Forex (foreign exchange trading)?
Answer: Currency Trading For Dummies, no offense. The "For Dummies" series is well known for its expertise in every field one can imagine.

That said, what prompts you to want to get into this? The average person is very likely to lose money as the long time experts walk away winners. Do you have an urge to trade commodity futures? I sure don't. 

While I offer the book as a guide, the real answer is "you shouldn't."