Let $a \in \mathbb{R}$ and the series
$x_1=1;$
$n \in \mathbb{N^*};$
$x_{n+1} = x_n + \sqrt{x_n^2 + 1};$
Calculate: $\lim_{n\to\infty}(\frac{2^n}{x_n})$
Please do not post a proof to this because I only want a hint.
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Also: https://math.stackexchange.com/q/1175041/42969 and some more, which can be bound with Approach0 – Martin R Nov 10 '19 at 09:53
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I just want a hint not a proof. – Marc Grec Nov 10 '19 at 09:53
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The first equations in https://math.stackexchange.com/a/1465632/42969 and https://math.stackexchange.com/a/1178287/42969 are hints. – Martin R Nov 10 '19 at 09:54