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-

Question Number 107946 by ZiYangLee last updated on 13/Aug/20

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 .