A sequence $\{x_n\}$ is given by $x_n= a_n-\sqrt{2n}$ and $a_n$ is given by $a_1=1$ and $a_n=a_{n-1}+\frac{1}{a_{n-1}}$.
Please help. I could not find a way out.
Is the sequence $x_n$ convergent, where $x_n= a_n - \sqrt{2n}$ and $a_n=a_{n-1}+\frac{1}{a_{n-1}}$
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real-analysis
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0http://math.stackexchange.com/questions/1540572/upper-bound-of-a-n1-a-n-frac1a-n – 2017-02-15