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Uniformly convergent sequence

  1. Apr 20, 2008 #1
    I need to determine whether the sequence [tex]\{\frac{n^2x}{1+n^3x}\}[/tex] is uniformly convergent on the intervals:

    [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?
  2. jcsd
  3. Apr 21, 2008 #2


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    Science Advisor

    The general idea is that for a>0, there will be an N such that the sup of the sequence will be at x=a for n>N.
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