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That’s a quirky problem; offhand, if the limit, L, exists then log of the limit exists and in particular the log of the limit is the limit of the log of the expression, which in this case yields log L = -log (e^n) + log(Sum_k_n (n^k/k!)); which gives the condition that L is between 0 and 1; in fact it seems to me that it says L= 1, since that’s wrong I must have made a bad turn somewhere, perhaps these logs cancel in some non trivial way to get L=.5, idk.
Weird, glad you solved it though. Maybe I should send this one to my math advisor he’s an analyst, I bet he does this stuff with his eyes closed.
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