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: 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


    User Avatar
    Science Advisor
    Homework Helper

    Write it as (1+2x)+(1+2x)x^2+(1+2x)x^4+...Now do you see what you are missing?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted