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If \[\left\{a_n\right\}\mid n\geq 0,a_1=5,a_{n+1}=a_n^22,n\in\mathbb{R}\] find \[\lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_1a_2\cdots a_n}\].
 2 years ago
 2 years ago
If \[\left\{a_n\right\}\mid n\geq 0,a_1=5,a_{n+1}=a_n^22,n\in\mathbb{R}\] find \[\lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_1a_2\cdots a_n}\].
 2 years ago
 2 years ago

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Mr.MathBest ResponseYou've already chosen the best response.1
This is just a guess: \(\large \frac{23}{5}\)?
 2 years ago

badreferencesBest ResponseYou've already chosen the best response.0
\(\sqrt[2]{21}\) actually.
 2 years ago

Mr.MathBest ResponseYou've already chosen the best response.1
You didn't need to write the answer! .
 2 years ago

Mr.MathBest ResponseYou've already chosen the best response.1
Okay. I will try to write a proof for that.
 2 years ago

badreferencesBest ResponseYou've already chosen the best response.0
Oh, haha. XD Apparently, the problem can be solved using repeated telescopy \(a+\frac{1}{a}=5\Rightarrow x_{n+1}={a^2}^n+\frac{1}{{a^2}^n}\), but I'm not sure I understand what they're getting at with this hint.
 2 years ago
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