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?

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# Uniformly convergent sequence

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