Prove that the sequence $a_n$ of positive numbers such that $a_n=\sqrt {a_ {n-1}a_ {n-2}} $, $n>2$ converges. Find its limit.

Asked Jan 23 '23 at 13:13

Active Jan 23 '23 at 13:17

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Here according to given condition $a_2$ shouldn't exist as $a_1$ and $a_0$ do not exist, which makes the existence of entire sequence dubious. Please someone correct where I'm wrong.

edited Jan 23 '23 at 13:17

QC_QAOA

11,796

asked Jan 23 '23 at 13:13

Puneet Mishra

1

Please edit your post to make your formula readable and inside the text, not only in the title. – Anne Bauval Jan 23 '23 at 13:16
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Since the relation is for $n>2,$ the two first terms $a_1$ and $a_2$ are supposed to exist. – Anne Bauval Jan 23 '23 at 13:21

Prove that the sequence $a_n$ of positive numbers such that $a_n=\sqrt {a_ {n-1}a_ {n-2}} $, $n>2$ converges. Find its limit.

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