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How to finish this proof

  1. Dec 2, 2008 #1
    |(n^2 +10)/(n^3 -10)<(n^2 +10)/(n^3)< ..<e

    i need some (1/n)<e

  2. jcsd
  3. Dec 2, 2008 #2
    What's the actual question that you're asking?
  4. Dec 2, 2008 #3
    i need to prove a convergence

    i stuck on the last part
    i got


    what to write about N ??
  5. Dec 2, 2008 #4
    To show it is bounded:

    0 < |(n^2 +10)/(n^3 -10)<2(n^2)/(n^2) = 2

    To show it converges, try to show that the sequence is monotone, and use the fact that all bounded and monotonic sequences converge. Or, see below:

    To show it converges:

    [n^2(1 + 10/n^2)] / [n^2(n - 10/n^2)]

    = (1 + 10/n^2) / (n - 10/n^2)

    the 10/n^2 in both the numerator and denominator converge to 0 and so we have 1/n, which converges to 0 as well.
    Last edited: Dec 2, 2008
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