# I know it is convergent by I cannot determine why

1. Dec 24, 2009

### golb0016

1. The problem statement, all variables and given/known data
0 to infinity sum of 6/(4n-1)-6/(4n+3)
Determine if the series is convergent or divergent.

3. The attempt at a solution
I know it is convergent by I cannot determine why.

2. Dec 24, 2009

### Dick

Re: Convergence

Did you try to see if it might be a telescoping series?

3. Dec 24, 2009

### jgens

Re: Convergence

With some algebra, you should be able to show that the series converges. For example, with the particular series in question we can show that:

$$\frac{6}{4n -1} - \frac{6}{4n + 3} = 6 \left(\frac{(4n + 3) - (4n - 1)}{(4n + 3)(4n - 1)}\right) = 6\left(\frac{4}{(4n + 3)(4n - 1)}\right)$$

Using a little bit more algebra, you should easily be able to determine that the series is convergent.

Edit: Oops, somebody got here first. Sorry Dick!

4. Dec 24, 2009

### Dick

Re: Convergence

Apologies never necessarily. Besides, you showed how a similar series would converge even if it doesn't telescope using a comparison test. That's a different answer.