I need to determine whether the sequence [tex]\{\frac{n^2x}{1+n^3x}\}[/tex] is uniformly convergent on the intervals:(adsbygoogle = window.adsbygoogle || []).push({});

[1,2]

[a,inf), a>0

For the first one, I notoced the function is decreasing on the interval, so the [tex]\sup|\frac{n^2x}{1+n^3x}|[/tex] will be when x=1, and when x=1, the sequence goes to 0, proving uniform convergence.

I'm not so sure how to approach the second one, because the sequence may not necessarily be decreasing on [a,inf)

Any help?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Uniformly convergent sequence

**Physics Forums | Science Articles, Homework Help, Discussion**