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Determine whether the sequence converges or diverges and find the limit

  1. Apr 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine whether the sequence an = 11/n2 = 21/n2 + ... + n1/n2 converges or diverges. If it converges, find the limit.

    2. The attempt at a solution

    I have no idea what to do with this problem. I don't see why I can't simplify n/n^2 to 1/n. It was suggested to me to factor out 1/n and introduce the variable i (from Riemann Sums), but I don't see how that helps (and I don't see how I would just introduce i anyway).
     
  2. jcsd
  3. Apr 15, 2012 #2

    Dick

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    Factor out the 1/n^2. Can you write an expression for the sum (1+2+...+n)?
     
  4. Apr 15, 2012 #3
    I'm not really sure what you mean.
     
  5. Apr 15, 2012 #4

    Dick

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    I meant pretty much what I said. an=(1/n^2)*(1+2+...+n), right? Perhaps you know a formula for (1+2+...+n) in terms of n? If not, and you know how to integrate you can also do it as a Riemann sum. Can you write down a Riemann sum for the function f(x)=x between 0 and 1?
     
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