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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

    jambaugh

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    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.
     
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