Exercise 1.3 of Lawler, Random Walk and the Heat Equation, is to show there exists a $c>0$ such that for every real real $r$ and every integer $n$, $$ e^{-cr^2/n}\le e^r(1-r/n)^n\le e^{cr^2/n} $$ There seems to be some typo; when $r=n=1$ the middle term is $0$ whereas the supposed lower bound is always $>0$. I am looking for a correct statement of what I'm guessing is a well-known inequality (or a clarification of how I'm misinterpreting things). I'm not looking for a proof (yet).
2026-03-25 12:13:09.1774440789
bounds on e convergence
31 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CALCULUS
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