"Let [tex]k\in \mathbb{N}[/tex] and [tex]a_0=k[/tex]. Let [tex]a_n=\sqrt{k+a_{n-1}}, \forall n\geq1[/tex] Prove that [tex]a_n[/tex] converges."(adsbygoogle = window.adsbygoogle || []).push({});

If we look at the similar sequence b_0 = k and b_n = sqrt(a_n-1), then that sequence obviously converges to 1. Unfortunately, b_n<a_n so I can't use the squeeze theorem.

Any hints would be nice.

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# Homework Help: Convergence of a Sequence

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