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Important Fact?

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Important Fact?

JMyers
Re: "College Algebra", p. 682, last full paragraph and footnote #2.  Forgive my ignorance, but I'm having trouble recognizing the importance of the fact that the limit as n approaches infinity of x-to-the-n (over) n-factorial equals 0.  Can you please enlighten me?  Thanks in advance for the help, and a big THANKS for a most awesome precalculus textbook!
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Re: Important Fact?

Carl Stitz
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In Calculus, this fact can be used to show the infinite series:  sum x^n / n! from n = 0 to infinity adds up (converges) to a number for all x... this leads to all sorts of amazing mathematics (which I won't spoil for you!) Thanks for reading!

Carl
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