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 November 20th, 2013, 07:33 AM #1 Member   Joined: Jan 2013 Posts: 96 Thanks: 0 Limit 2 Let $(a_n)_{n \ge 1}$ be a convergent sequence. If $\lim_{n \to \infty} \frac{\sqrt{a_1^4+...+a_n^4}}{\sqrt{a_{n+1}^2+...+ a_{2n}^2}+\sqrt{n}}=\frac{1}{2}$, find $\lim_{n \to \infty} a_n$.
 November 20th, 2013, 10:25 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Limit 2 You can find the answers by assuming the sequence is constant. You should be able to turn this into a rigorous proof if you sprinkle in enough epsilons and deltas. I get -1/2 and 1 as the answers FWIW. Probably the answer key only mentions the latter.
November 22nd, 2013, 10:51 AM   #3
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Re: Limit 2

Quote:
 Originally Posted by CRGreathouse You can find the answers by assuming the sequence is constant. You should be able to turn this into a rigorous proof if you sprinkle in enough epsilons and deltas. I get -1/2 and 1 as the answers FWIW. Probably the answer key only mentions the latter.
I get 1 as the answer. The limit of the function if the sequence converges to -1/2 is 1/6.

 November 23rd, 2013, 08:42 AM #4 Member   Joined: Jan 2013 Posts: 96 Thanks: 0 Re: Limit 2 Any solution, please?

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