How to find the limit of this fraction? | Chinese Math Competition | limit problem in Calculus

Can you evaluate the limit of this fraction of factorials? We'll introduce the Sandwich method and use it to solve this limit problem. This is a math competition question.

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[john]

Great solution! Thank you for sharing!

[nightbot.]

At first I presumed it probably wasn't 1 because usually the obvious answer isn't correct in these kinds of problems. But when I divided the numerator and denominator by n! I got a polynomial expression with highest terms n^n on top and bottom of fraction so it actually equals 1

[nasrullahhusnan]

I work on the concept of factorial and limit as follows:
Let x=[1!+2!+3!+...+(n-1)!+n!]/n!


It clear that as n goes to infinity then x closer and closer to n. Thus lim(x)=1 as n-->infinity. Hence x=1.

[abiedarkham]

since lim n (n-1)!/n! = 0, so lim Sn / n! = lim n! / n! = 1, is it?

[billbill]

Just divide up and down with n! and it is done