# Series - help.

1. Nov 2, 2007

### frasifrasi

I am trying to practice for an exam but can't do this question:

does the series $$\((-1)^n/ln(n)$$ from n = 2 to infinity converge abs/conditionally/diverge?

I know if a do an alternating series test, the integral will converge because lim goes to 0 and a(n+1)<an.

But how can I prove that it's conditionally convergent? I did the limit test but it says that it is absolutely convergent, which is not the answer(it is supposed to be conditionally).

Thank you...

Last edited: Nov 2, 2007
2. Nov 3, 2007

### Gib Z

Well it can't be absolutely, because 1/( ln n ) goes to 0 much slower than another well known series that diverges doesn't it?

Last edited: Nov 3, 2007
3. Nov 3, 2007

### frasifrasi

ok, 1/n diverges as is a bigger series, so 1/ln(n) must also converge, right?

4. Nov 3, 2007

### SiddharthM

write it with inequalities and using the definition of "diverge" show that 1/n FORCES 1/lnn to blow up.

5. Nov 3, 2007

### frasifrasi

Sorry I meant, since thesmaller series diverges, 1/ln(n) will also diverge.

6. Nov 3, 2007

### HallsofIvy

Staff Emeritus
And since 1/ln n is a decreasing sequence, the "conditional convergence" part is easy!