Homework Help: Rules for monotone sequences?

1. Jun 30, 2011

cnwilson2010

1. The problem statement, all variables and given/known data
Let an be monotone sequences. Prove or give a counterexample:

The sequence cn given by cn=k*an is monotone for any Real number k.

The sequence (cn) given by cn=(an/bn) is monotone.

2. Relevant equations

3. The attempt at a solution

On the first one, I don't think the change of sign on k can change the "monotoneness" of the sequence other than by changing decreasing to increasing and vice versa.

I have played around using different sequences to see if this is true and it is looking like it is, but I just feel that it could be false.

Any ideas?

Last edited: Jun 30, 2011
2. Jun 30, 2011

lanedance

for the first calculate the difference between terms and show it is always either pos or neg

2nd find a simple counter example, consider an alternating series

3. Jun 30, 2011

cnwilson2010

I neglected to put the condition that bn is also monotone.

So I was thinking of an with a different sign than bn but this doesn't seem to change much either.