Let a sequence {a_n } satisfies a_n = { ((2, n=1)),((2ln(a_(n−1) )+(1/a_(n−1) ) , n≥2)) :} Prove that a


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Question Number 107946 by ZiYangLee last updated on 13/Aug/20
$Let a sequence {a_n } satisfies a_n = { ((2, n=1)),((2ln(a_(n−1) )+(1/a_(n−1) ) , n≥2)) :} Prove that a_n ≥1+(1/n) for all n∈N.$
$Let a sequence {a_{n}} satisfies$ $a_{n} = {\begin{cases} 2, n = 1 \\ 2 \ln (a_{n - 1}) + \frac{1}{a_{n - 1}}, n ⩾ 2 \end{cases}$ $Prove that$ $a_{n} ⩾ 1 + \frac{1}{n} for all n \in N .$
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