1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Simple Series

  1. Jan 27, 2008 #1
    1. The problem statement, all variables and given/known data

    How can I simplify sum from j=0 to infinite of x^(2j) ?

    2. Relevant equations

    3. The attempt at a solution
    THis is close to the geometric series but I'd have to square each individual term
  2. jcsd
  3. Jan 27, 2008 #2
    well this looks like a gjeometric series, it will diverge for IxI>1, and it will converge for 0<IxI<1

    what else are u looking for?
  4. Jan 27, 2008 #3
    Look at its partial sums, take the limit and you will get the result, i mean where it converges to for 0<IxI<1
  5. Jan 27, 2008 #4
    Ignore what i just said, in my posts #2,3
    EDIT: Well don't ignore them, they seem to be right. Can you go from there?
    Last edited: Jan 27, 2008
  6. Jan 27, 2008 #5


    User Avatar
    Science Advisor
    Gold Member

    You might also observe that [itex]x^{2j} = (x^2)^j [/itex] so start with the problem [itex]\sum_{j=0}^\infty a^j[/itex]
    and later set [itex] a = x^2[/itex]

    while you're at it recall how to factor differences of higher powers, e.g. [itex] a^5 - 1 = [/itex]? There's a key formula you'll need.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook