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MATHEMATICS Convergent sequence
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Exercise 84: Calculate the limit
.Solution: Please, note that
We use the theorem:
Theorem: If for a sequence
we have 
,where q >1 and an > 0 for n =1, 2,... , then
. We get
Using the definition of n! = n * (n-1) * (n-2)
* ... * 2 * 1, so n! = n * (n-1)!, and using
the definition of the number e
(
)
. We get
Therefore
Using the theorem, we get
