I'm struggling with a growth model and finding a formula to describe the growth.
I've managed to figure out $a_n = an^{log_b(n)}$ but now need to find a formula for the sum of the series $S_n = f(n)$
Thanks in advance,
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1The series is divergent. Do you mean a sum from $n=1$ to $n=N$? – Raffaele Sep 29 '17 at 07:33
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Yes, thank you! – Ishai Smadja Sep 29 '17 at 08:37
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I think I should be able to use Stirling's approximation in some way, but haven't managed to reach something with $log(n!)$ – Ishai Smadja Sep 29 '17 at 08:55
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So you are looking for $$S_n=a,\sum^n_{k=1}e^{\ln^2k/\ln b}$$ essentially, is that correct? There is certainly no closed expression, but an approximation should be possible. – Sep 29 '17 at 10:17