- #1

kathrynag

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## Homework Statement

Asssume (an) is a bounded sequence with the property that every convergent subsequence of (an) converges to the same limit a. Show that (an) must converge to a.

## Homework Equations

## The Attempt at a Solution

If the subsequence converges to a we have , we have:

[tex]\left|ank-a\right|[/tex]=a.