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: How do I counter support Zyra?
Answer: Look for best counters to Zyra her: http://www.picklol.net/zyra, so I would pick Lux against her. because of stun and harras!