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Find a closed form for this sequence: $a_{n+1} = a_n + a_n^{-1}$
If a sequence is defined as $ a_{n+1}=a_{n}+\frac{1}{a_{n}} $
where $a_1 = 1$
Find the general value of $a_n$ as $f(n)$
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1What is $a_0$ ? – Teddy Oct 17 '12 at 07:14
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So you're looking for a closed (non-recursive) form for your $a_n$. To get there, you're really going to need an initial value ($a_0$ or $a_1$), as Teddy points out. – Cameron Buie Oct 17 '12 at 07:15
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Hey! I included the required initial value. – Oct 17 '12 at 07:27
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and also this http://math.stackexchange.com/questions/10065/ – Oct 17 '12 at 07:42
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I don't believe it exists, see:
ajja
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But no answer seems to justify the generalization of that sequence or how it came. – Oct 17 '12 at 14:10