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Homework Help: Fourier Analysis - uniform convergence on (-inf, inf)?

  1. Jan 21, 2009 #1
    I have a question that I just don't know how to go about.

    " Let Fn = x/(1+(n^2)(x^2)) where n=1,2,3,... show that Fn converges uniformly on (-infinity,infinity)"

    To be honest, I don't even know where to start. Is this a series? How would I solve this. Would the Abel's test apply?
     
  2. jcsd
  3. Jan 21, 2009 #2
    Try using the ratio test to determine if a series converges.

    [tex]lim\frac{F_{n+1}}{F_{n}}[/tex]

    Take this limit for n approaches infinity and for n approach negative infinity
     
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