# Series and Sequences

1. Feb 29, 2008

### STLCards002

Can somebody please explain to me:
How both series and sequences converge, and the various tests to find out.

I've tried searching but it seems impossible to get any explainations as to why you do the specific test.

2. Feb 29, 2008

### quasar987

There isn't. You just try them one by one. Except after a while you develop an intuition as to which test will work on which series.

It's like integration. After a while you see whether integration by parts will be fruitful or not.

3. Mar 1, 2008

### HallsofIvy

Staff Emeritus
There are no general rules that say "apply this test to these kinds of problems". You try one and if it doesn't work you try another.

4. Mar 1, 2008

### STLCards002

Well can you list the various tests that I can try to apply

I understand the a$$_{}n+1$$/a$$_{}n$$ test where if the ratio is > 1 and it is bounded about then the sequence converges and < 1 and bounded below then it converges. But I don't understand the reasoning behind the other ones.

Those should be subscripts sorry...

Last edited: Mar 1, 2008
5. Mar 1, 2008