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?
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?
You need to understand that in a positive-term series, if for all n, then .
Now if is convergent, that means it can be equated to a number, and so anything less than or equal to it is also a number. Therefore will also be convergent.
Meanwhile, if is divergent, it means that the series will shoot off to . Anything greater than or equal to this will also shoot of to (quicker), and so is also divergent.
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!