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

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

Try using the ratio test to determine if a series converges.

$$lim\frac{F_{n+1}}{F_{n}}$$

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