Determine whether the sequence converges or diverges and find the limit

  • Thread starter Sean1218
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  • #1
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Homework Statement



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).
 

Answers and Replies

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