Real Analysis: Sequences and Series

[sprstph14]

Suppose that a_k is a decreasing sequence and (a_k) approaches 0. Prove that for every k in the natural numbers, a_k 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?

 

[LCKurtz]

Suppose that a_k is a decreasing sequence and (a_k) approaches 0. Prove that for every k in the natural numbers, a_k 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?

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 a_k < 0. You should be able to get an easy contradiction.

 

[sprstph14]

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