# Math Help - Series Convergence

1. ## 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.

2. ## Re: Series Convergence

Just off the top of my head, and without being exactly sure what you're asking, could you try $a_{n} = \frac{1}{b_{n}^{2}}$?

3. ## Re: Series Convergence

bn = ln(x)
1/bn^2 = 1/ln(x)^2 => Does not converge (The first property required)

4. ## Re: Series Convergence

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!

.