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The recursive formula is the following:

$a_n = \left(\dfrac{2n^4 - 1}{1 + 3n^4}\right) a_{n+1}$ ; $a_1 = 1 $

In which fundamentals need I to base me for solving this?

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You can use the following loose-ish bound: for all $n\geq 1$, $$ \frac{3n^4+1}{2n^4-2} \geq \frac{3}{2} $$ so $a_{n+1} \geq \frac{3}{2}a_n$ for all $n\geq 1$.

More (place your mouse over the gray area to reveal its contents):

By induction, show that $$a_n\geq \left(\frac{3}{2}\right)^{n-1}.$$

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  • $\begingroup$ All too easy. ;-)) +1 $\endgroup$
    – Mark Viola
    Feb 26, 2016 at 4:51
  • $\begingroup$ @Dr.MV "I like my math problems like I like my eggs." $\endgroup$
    – Clement C.
    Feb 26, 2016 at 5:01
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    $\begingroup$ As long as the answers aren't "poached." Yes I just wrote that! ;-) And I hope that cracked you up. Ouch. $\endgroup$
    – Mark Viola
    Feb 26, 2016 at 5:10

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