- #1

- 346

- 3

## Main Question or Discussion Point

My textbook explains how the limit of x^n/(n!) as n→∞ equals 0, x ∈ ℝ. Since a(n) = x^n/(n!) and a(n+1) = x^(n+1)/((n+1)n!) and (a(n+1))/a(n) = x/(n+1) and lim n→∞ x/(n+1) = 0, then it seems obvious.

But, I went on Wolfram Alpha and I noticed that when I made x = n and put in some large values, x^n increased much faster than n! did. Is this just one of those weird outcomes of using infinity? Or why does infinity change the regularity of the sequence so much to the point that they invert?

But, I went on Wolfram Alpha and I noticed that when I made x = n and put in some large values, x^n increased much faster than n! did. Is this just one of those weird outcomes of using infinity? Or why does infinity change the regularity of the sequence so much to the point that they invert?