10-2-61 factorial and power problem
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Limit as N goes to Infinity of N factorial over one O 3 to the
north power.
We could think of this as the limit as N goes to Infinity of n
* n - 1 * n - 2 * n - 3...
dot .321.
That's what our N factorial means.
And then we have one O 3 * 1 O 3 * 1 O 3 * 1 O 3 N times in the
denominator.
So we could actually look at each of these terms n / 103
times and -1 / 103 times and -2 / 103.
Well, if I put in something really, really big, I'm going to
get Infinity times Infinity times Infinity.
And as we go down 3 / 103, two over 103, one over 103 are
constants.
They're going to be small numbers, but they're going to be
constants.
So if I have Infinity times anything, it's still going to be
Infinity, and thus it's going to diverge.