I'm studying for the GRE thats coming up in a week or two and I came across a problem where the answer given in the book does not make sense to me and I was wondering of someone here could explain it to me.(adsbygoogle = window.adsbygoogle || []).push({});

Question:

Lim as n goes to infinity of X_(n+1) / X_n

Where X_n = n^n / n!

Answer:

So I started by simplifying the expression down to:

Lim as n goes to infinity of (1 + 1/n)^n

The book informs me and by some proofs online that this tends toward e. However I was hoping someone could explain this to me because from my point of view it should just hit 1.

Since 1/n -> 0, 1+0 = 1, and 1^n is 1 for any arbitrarly high power.

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# Homework Help: Limit Question

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