General question on proving the convergence of a series

Sorry no specific example here but I was just wondering if it's mathematically correct to prove that a series is convergent by comparing it to another series that is larger than it and use an integral test on that larger series to prove that it is convergent.

I ask this because all the examples I have seen of the "comparison test" try to compare that series to a series in the "p-series form" where you can tell straight away if it's convergent by looking at the power of the bottom variable. The problem is that I have trouble finding proper comparisons because I get all confused. So is it wrong if I use both a comparison and an integral test in unison?

Re: General question on proving the convergence of a series

Hey jgv115.

You can do this but you should outline the type of series. For example is an alternating series or are all terms the same sign?

Re: General question on proving the convergence of a series

Re: General question on proving the convergence of a series

Hi chiro,

Yes they are all the same sign. I am aware of the tests required for an alternating series!

Thanks for your confirmation.

edit: Yep, I understand, Prove it!

Re: General question on proving the convergence of a series

Remember than when using the first comparison test which prove it mention both series must be the sum of positive terms.

Re: General question on proving the convergence of a series

Quote:

Originally Posted by

**Shakarri** Remember than when using the first comparison test which prove it mention both series must be the sum of positive terms.

And if your series is not all positive term, you can test the series of absolute values against another series. If a series is absolutely convergent, then it is still convergent.

Proof:

and so by the comparison test, if is convergent, therefore so must be .