Paul M. answered • 08/25/19

BS Mathematics, MD

I can help you with 2 parts; I don't see how to use the "Squeeze" Theorem in the 3rd part.

1-(1/n)=(n-1/n)

Substitute n=k+1 and

[1-(1/n)]^{n} becomes [k/(k+1)]^{k+1} = {1/[1+(1/k)]}^{k+1} = [1+(1/k)]^{-k-1}

I think this last expression = e^{-1'}

lim n->∞ n!/n^{n} = 0 at least one of the factors in the quotient (1/n) goes to 0 as n goes to ∞ and at worst all

the other terms approach 1. I'm not sure how the first 2 parts are related to the 3rd, nor do I see how to use the so-called "Squeeze" Theorem in this case.

I"m sorry I cannot be more helpful.

Paul M.

08/26/19

Nicholas R.

Thank you very much for your help!08/26/19