- #1

kehler

- 104

- 0

## Homework Statement

Suppose that the sequence {a

_{n}}converges. Show that the sequence {a

_{n}} is bounded.

## The Attempt at a Solution

Since the sequence converges, for every delta>0, there must exist a number N such that for every n>=N,

|a

_{n}- x|< delta. Therefore, for n>=N, -delta+x < a

_{n}< delta + x.

So I've proven that for n>=N, the sequence is bounded between -delta+x and delta+x.

But I don't know how to prove that for n<N, a

_{n}is also bounded. I know that there are only a finite number of elements before the sequence starts to converge. Is there a theorem stating that all finite sets are bounded?