Fourier Analysis - uniform convergence on (-inf, inf)?

  • Thread starter Tacos
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  • #1
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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?
 

Answers and Replies

  • #2
288
1
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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