Example 1.9 Given a positive sequence {an}nzo satisfying √a √ão + 1 and an+1 for any positive integer n, show that an-1

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Example 1 9 Given A Positive Sequence An Nzo Satisfying A Ao 1 And An 1 For Any Positive Integer N Show That An 1 1 (32.81 KiB) Viewed 22 times

Example 1.9 Given a positive sequence {an}nzo satisfying √a √ão + 1 and an+1 for any positive integer n, show that an-1 an+1 an < 1 converges as n →∞. Show moreover that an0n converges as n→ ∞, where 0 is the limit of the sequence an+1/an.