What is the exact formula for $a_n$ in the sequence $a_{n+1} = 2a_n + 1/a_n, a_1=1$? I discovered that there are no elementary answers, but I don't know how to solve it.
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what is the first term? – Asinomás Aug 08 '15 at 17:02
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The first term is one. I forgot to add that. Thank you. – Henricus V. Aug 08 '15 at 17:03
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I don't get it. You know in advance that no nice closed form exists, and you are asking for a closed form? – Jack D'Aurizio Aug 08 '15 at 17:11
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maybe he meant that he knows there is no very simple way to get the closed formula. – Asinomás Aug 08 '15 at 17:12
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I am asking for the equation for $a_n$. Calculus is allowed so its not a closed form. – Henricus V. Aug 08 '15 at 17:13
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There's a closed form don't worry ^^ – Oussama Boussif Aug 08 '15 at 17:33
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2I've just checked that answer it seems to be wrong :/ – Oussama Boussif Aug 08 '15 at 17:41
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3Yup, the most upvoted answer there is wrong, – achille hui Aug 08 '15 at 17:48