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Finding limit of a sequence

  1. Oct 25, 2011 #1
    I've been trying to learn some maths by myself. A book I found starts with a section on limits. I feel that I have a decent understanding of what is written, but then, there are some problems given that I just can't figure out. I feel like I'm missing something basic. I'm not sure what I'm looking for. Maybe a resource with some examples of how to solve different kinds of equations would be enough. I'd also appreciate it if you could show how to solve a couple of problems I'm having a hard time with:

    [itex]lim\sum\limits_{k=1}^{n-1} \frac{k^{2}}{n^{3}}, n\geq 2[/itex]


    [itex]lim\sum\limits_{k=2}^n \frac{k-1}{k!}, n\geq 2[/itex]
  2. jcsd
  3. Oct 25, 2011 #2


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    For the first one, take 1/n3 outside the summation, the sum over k2 is readily available [ (n-1)n(2n-1)/6 ], so the limit will be 1/3.

    For the second split it into two sums (k and -1 numerators). Compare them with each other. The final answer will be 1 (unless I made a mistake).
  4. Oct 26, 2011 #3
    Thanks a lot, I see now.
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