(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that the sequence {a_{n}}converges. Show that the sequence {a_{n}} is bounded.

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Prove that a converging sequence is bounded

**Physics Forums | Science Articles, Homework Help, Discussion**