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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 $f(n)$

Thanks

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What is $a_0$ ? –  Teddy Oct 17 '12 at 7:14
    
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 7:15
    
Hey! I included the required initial value. –  Sai Krishna Deep Oct 17 '12 at 7:27
    
and also this math.stackexchange.com/questions/10065 –  user17762 Oct 17 '12 at 7:42
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marked as duplicate by Did, Marvis, Hans Lundmark, Noah Snyder, Thomas Oct 17 '12 at 14:09

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1 Answer

I don't believe it exists, see:

http://oeis.org/A073833

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But no answer seems to justify the generalization of that sequence or how it came. –  Sai Krishna Deep Oct 17 '12 at 14:10
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