(adsbygoogle = window.adsbygoogle || []).push({}); 1. Let a_{0}and a_{1}be positive real numbers, and set a_{n+2}= sqrt(a_{n+1}) + sqrt(a_{n}) for n [tex]\geq[/tex] 0.

(a) Show that there is N such that for all n [tex]\geq[/tex] N, a_{n}[tex]\geq[/tex] 1.

(b) Let e_{n}= |a_{n}−4|. Show that e_{n+2}[tex]\leq[/tex](e_{n+1}+e_{n})/3 for n[tex]\geq[/tex] N.

(c) Prove that this sequence converges.

Can someone please give me some hints to start with a)? Thank you in advanced.

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# Homework Help: Limit of sequence

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