# Series Convergence

• Jun 1st 2013, 08:15 AM
MichaelEngstler
Series Convergence
Hello,
I have a statement I must prove or disaprove with a counter example, The statement is:
For each series bn that goes to infinity (bn -> inf), exists a series an that has both of these properties:
1.The series an converges
2.The series an*bn diverges.

My intuition says the statement is true, but Im struggling proving it.

Thanks a lot,
Michael.
• Jun 1st 2013, 10:19 AM
nimon
Re: Series Convergence
Just off the top of my head, and without being exactly sure what you're asking, could you try $\displaystyle a_{n} = \frac{1}{b_{n}^{2}}$?
• Jun 1st 2013, 10:43 AM
MichaelEngstler
Re: Series Convergence
bn = ln(x)
1/bn^2 = 1/ln(x)^2 => Does not converge (The first property required)
• Jun 1st 2013, 11:19 PM
zzephod
Re: Series Convergence
Quote:

Originally Posted by MichaelEngstler
Hello,
I have a statement I must prove or disaprove with a counter example, The statement is:
For each series bn that goes to infinity (bn -> inf), exists a series an that has both of these properties:
1.The series an converges
2.The series an*bn diverges.

My intuition says the statement is true, but Im struggling proving it.

Thanks a lot,
Michael.

Are you talking about series or sequences, they are not the same thing!

.