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MATHEMATICS Convergent sequence
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Exercise 89: Calculate the limit
.Solution: We use the theorem: Theorem: If for a sequence
we have 
,
where q >1 and an > 0 for n
=1, 2,... , then
.
We get (
). Therefore
Using the definition of n! = n * (n-1) * (n-2) * ... * 2 * 1, so n! = n * (n-1)!, we get
Therefore
.
Thus
