Thursday, April 7, 2016

sequences and series - Weird limit limlimitsnmathoptoinftyfrac1ensumlimitsnkmathop=0fracnkk!




limn1ennk=0nkk!




I thought this limit was obviously 1 at first but approximations on Mathematica tells me it's 1/2. Why is this?


Answer



In this answer, it is shown that
ennk=0nkk!=1n!nettndt=12+2/32πn+O(n1)


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