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 Mar 9 accepted Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$ Mar 9 comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$ @RobertIsrael: Phew - now I can drink the coffee slowly, rather than chugging it. That helps a huge amount, much appreciated! Mar 9 comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$ @RobertIsrael: Thanks much. There are still (at least) two things I'm not getting. You say $\exp(n \log(1-p^k)) \approx \exp(n p^k)$, shouldn't it be $\exp(n \log(1-p^k)) \approx \exp(-n p^k)$ (negative sign)? And why are we solving $npk \approx 1$ Since this is the size of the term $f(k,n)$, wouldn't we want it to be $\exp(n p^k) \approx 1$? Mar 9 comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$ @RobertIsrael: Thanks for the helpful comments. I too had thought about splitting the summation into two parts, one with terms close to zero, the other with terms close to one, but didn't see how to choose the splitting point appropriately. How did you decide on $\frac{\log n}{\log\frac{1}{p}}$? Mar 8 asked Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$ Feb 23 answered Examples to show intersection of two uncountable sets can be countably infinite Feb 7 answered Confused about permutation cycles - Question on joint cycles of odd length Feb 1 answered Popular math books with depth Oct 22 awarded Yearling Sep 8 answered Central limit theorems, Almost sure invariance principles and Brownian motion Aug 23 answered Introduction to Information Theory Jul 25 comment Help solving: Problem on Normal Distribution of Data Clearly this is a fictional example. Phone call durations do not come from a normal distribution - calculate the probability that a call takes less than 0 seconds, it is not zero! Jun 22 answered Is Aluffi's book a good second text for Algebra? Jun 22 answered Reference for Ergodic Theory May 26 answered What is a good complex analysis textbook? May 10 comment Need good material on multifractal analysis When I read it, I already knew why multifractals were interesting and what I needed to analyze & why. What I needed was the 'how', and I got that from this book. Riedi does have some interesting papers though, I remember really liking "The Multiscale Nature of Network Traﬃc: Discovery, Analysis, and Modelling". Also have a look at "Why study multifractal spectra?" by Peter Morters at people.bath.ac.uk/maspm/whystudy.pdf May 10 answered Need good material on multifractal analysis Mar 29 awarded Scholar Mar 29 comment How to show that $\sum\limits_{k=1}^{n-1}\frac{k!k^{n-k}}{n!}$ is asymptotically $\sqrt{\frac{\pi n}{2}}$? Thanks for all the help. I was expecting something simpler when they said " elementary asymptotic methods", but this will certainly do. Mar 29 accepted How to show that $\sum\limits_{k=1}^{n-1}\frac{k!k^{n-k}}{n!}$ is asymptotically $\sqrt{\frac{\pi n}{2}}$?