1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the sum of an infinite series

  1. Dec 4, 2009 #1
    Find the sum of the infinite series

    [tex]\sum _{n=1}^{\infty } \left( i /2\right) ^{2\,n}[/tex]

    I just can't seem to get started on this problem, so I was hoping somebody could give me a hint, as to what methods i should read up on.
     
  2. jcsd
  3. Dec 4, 2009 #2
    A good place to start would be to consider what (i/2)^2 is, that simplifies the sum considerably. You also need the formula for geometric series, that you can find for example from wikipedia.
     
  4. Dec 5, 2009 #3
    Actually, break i into its polar form which is [tex] i^2^n = e^i^n^(^p^i^) [/tex] . Now expand using Euler's identity and you are left only with [tex] cos\ n(pi) = (-1)^n [/tex] From there it is a geometric series.
     
  5. Dec 5, 2009 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Actually, there is no need to worry about "i". [itex](i/2)^{2n}= (i^2/4)^n= (-1/4)^n[/itex] so this is a purely real geometric series.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding the sum of an infinite series
Loading...