   Average Case Scenario
  Hello I was wondering if anyone could tell me what the mathematical trick is for evaluating a summation for only odd i/even i.  My summation would look something like this:summation from i = "odd index" to N 1/2^(i)summation from j = "even index" to N 1/2^(j + 1)I know there is a trick to be done I just can't remember it.  I know that for i to be odd it needs to be i = 2i + 1 and for even its just j = 2j.  If anyone has any suggestions that would be great.  Thank you.   