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Possible Duplicate:
Proof for convergence of a given progression $a_n := n^n / n!$

Is it fair to attack this problem as follows.

$$\frac1n\cdot\frac2n\cdots\frac{n-1}n$$

And the limit law allows for multiplication of each individual limit term.

So as $1/n$ converges to $0$, $0\cdot\ldots = 0$.

This is perhaps too simple, but why not ?

Anyway, I think my reasoning is plaussible, may the rule only count for determinate sequences. 1/n makes part of the sequence. So. It converges to 0.

5 Answers 5