Asymptotic of interesting recurrence relation

Asked Apr 24 '15 at 15:40

Active Apr 24 '15 at 17:03

Viewed 22 times

I want to study the asymptotic behavior of the following recurrence relation:

$y_1=1$;

$y_{n+1}=y_{n}+(1+\frac{y_n}{n})^{-n}\ \ $ for $n\ge 1$.

I made an initial attempt and guessed that $y_{n} \sim Log(n)$. Any referrence or hint about this might be helpful. Any help will be greatly appreciated

edited Apr 24 '15 at 17:03

Raphael

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asked Apr 24 '15 at 15:40

Jack

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Please lay out how/why the techniques laid our at our reference question don't help you. Given that you have a guess, have you tried proving it correct? Where did you get stuck? – Raphael Apr 24 '15 at 17:03
@Raphael. You might have been too quick on the trigger here. I don't see anything in the reference question that would help the OP with a problem like this. – Rick Decker Apr 24 '15 at 17:49
You might try asking this over on math.SE – Rick Decker Apr 24 '15 at 17:53

Asymptotic of interesting recurrence relation

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