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Explicit formula for a convergent series

  1. Apr 3, 2014 #1
    Hello PF.

    1. The problem statement, all variables and given/known data
    A function f is defined by f(x) = 1 + 2x + x2 + 2x3 + x4 + 2x5 + x6... Find the radius of convergence of the series and the explicit formula for f(x).


    2. Relevant equations



    3. The attempt at a solution
    I know that the formula for the series is going to be similar to the function xn2c, where c is some expression dependent on n that is equal to 1 when n is odd and equal to 0 when n is 0 or when n is even. However, I'm having difficulty finding what c actually is in terms of n. Maybe there's something obvious that I'm not seeing here?
     
  2. jcsd
  3. Apr 3, 2014 #2

    Dick

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    Write it as (1+2x)+(1+2x)x^2+(1+2x)x^4+...Now do you see what you are missing?
     
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