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- Feb 14, 2012
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Suppose \(\displaystyle \left({a_n}\right)_{n=1}^\infty\) be recursively defined by $a_0>1$, $a_1>0$ and $a_2>0$,
\(\displaystyle a_{n+3}=\frac{1+a_{n+1}+a_{n+2}}{a_n}\) for $n=0,1,2,\cdots$,
Show that $a_n$ has period of 8.
\(\displaystyle a_{n+3}=\frac{1+a_{n+1}+a_{n+2}}{a_n}\) for $n=0,1,2,\cdots$,
Show that $a_n$ has period of 8.