# Find a_n & b_n such that

1. Dec 22, 2014

### AfterSunShine

1. The problem statement, all variables and given/known data
Find $$a_n$$ & $$b_n$$ such that $$\sum_{n=0}^{\infty}a_n$$ & $$\sum_{n=0}^{\infty}b_n$$ are convergent series, but $$\displaystyle \sum_{n=0}^{\infty} \left( \sqrt{a_n} \cdot b_n \right)$$ diverges.

2. Relevant equations
None.

3. The attempt at a solution
Try too hard for this but still cannot find such $$a_n$$ & $$b_n$$.

2. Dec 22, 2014

### Staff: Mentor

That is not an acceptable post. You must show your efforts before we can offer tutorial help. Show us what you have tried so far please...

3. Dec 22, 2014

### AfterSunShine

There is nothing to show here
basically I tried a_n = 1/n^2 & b_n = (-1)^n / n but failed
tried a_n = 1/n^2 & b_n = arctan (1/n) but failed
and so on...

4. Dec 22, 2014

### Staff: Mentor

That is not so bad as a start. Can you modify the series in order to keep them converging, but doing so significantly slower?
And then you'll need some trick to get the product diverging - something that changes the sign flip thing...