- #1
wildman
- 31
- 4
Homework Statement
I am wondering if someone could give me some insight on how the following infinite series was derived:
[tex] P_e = \sum_{-\infty}^\infty (1/2)^{2|n|} = -1 + 2 \sum_{n=0}^\infty (1/2)^{2n} = 5/3 [/tex]
Homework Equations
See above
The Attempt at a Solution
I think the -1 comes when n = 0 and the 2 before the sum is because the absolute value of n makes the result symetrical around 0. That is why one can make the sum from 0 to infinity and multiply by 2. Right??
The second sumation must be equal to 4/3. Right? I guess my real question then is how do you find the closed form of this infinite series?