1. Apr 25, 2015

### sun1234

2. Apr 25, 2015

### micromass

Just because the $n$th term converges to $0$, doesn't mean the series converges. Unless you can explain better why it might imply this in this case.

3. Apr 25, 2015

### micromass

And the $p$-test only works for positive series (a series whose terms are positive).

4. Apr 25, 2015

### sun1234

That's what I think of. Also how do you know when to test for absolute converges and conditional converges? Thank you for trying to help.

5. Apr 25, 2015

### Staff: Mentor

Instead of answering that question, I think it would be a good idea for you to step back and take a closer look at the two tests you used, the p-series test and what you call the "nth term test."
As already stated, the p-series applies only to series consisting of positive terms. You also misused the other test that you used. What exactly does that test say?

6. Apr 26, 2015

### HallsofIvy

If a series "converges absolutely" then there is no point in asking if it converges conditionally. So it would seem to make sense to first try to show that a series converges absolutely and only if it doesn't try to show that it converges conditionally.

One test you do not mention is the "alternating sequence test": if, for $a_n> 0$, $\lim_{n\to 0} a_n= 0$ then $\sum (-1)^n a_n$ converges.