Let xn, yn be two convergent sequences. Show that limn-->∞xnyn exists.

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- Oct 5th 2010, 06:18 PMashamrock415Limit of two convergent sequences
Let xn, yn be two convergent sequences. Show that limn-->∞xnyn exists.

- Oct 5th 2010, 06:43 PMJhevon
Since the sequences converge, they have (finite) limits.

Let and

We will not only show that the limit of the product exists, but we will say what it is! We claim that

We need to show that for every , there exists an such that implies that

I will give you a hint how to proceed.

Note that

Now what can you say?