Prove an algorithm for logarithmic mean limn→∞an=limn→∞bn=a0−b0ln⁡a0−ln⁡b0

feminizmiki

feminizmiki

Answered

2022-01-19

Prove an algorithm for logarithmic mean limnan=limnbn=a0b0lna0lnb0

Answer & Explanation

nghodlokl

nghodlokl

Expert

2022-01-19Added 33 answers

You have several exact identities, such as an+1bn+1=an+bn2anbn=2n(a0b0), an+1bn+1=anbnanbn=(a0b0)2n The first tells us that if one of the sequences has a limit the other has the some limit. In combination bn can be eliminated to get, via mean value theorem, an=2n(a0b0)1(b0a0)2n=a0b0lna0lnb0+(2n)

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