# Real Analysis: Sequences and Series

1. Apr 13, 2010

### sprstph14

Suppose that ak is a decreasing sequence and (ak) approaches 0. Prove that for every k in the natural numbers, ak is greater than or equal to 0.

I was thinking I should assume the sequence is bounded below by 0 and do a proof by contradiction.

Any suggestions?

2. Apr 13, 2010

### LCKurtz

If you assume the sequence is bounded below by 0 you are assuming what you are trying to prove.

Just try an indirect argument. Assume some ak < 0. You should be able to get an easy contradiction.

3. Apr 13, 2010

### sprstph14

thanks. I guess I just really don't know what I'm doing.