# Determining if a series is convergent or divergent

• Jul 26th 2010, 03:48 PM
illidari
Determining if a series is convergent or divergent
Hi I was wondering if anyone could explain this to me,

I have

Series (-1)^n n/ln(n)
sum : infinite
n:2

I took the derivative and got : 1/ln(x) - 1/(ln(x)^2)

How do I determine if this is a decreasing or increasing function.

From what I could tell 2 is the only value to make it go <0 , so is this neither increasing or decreasing?
• Jul 26th 2010, 04:03 PM
tonio
Quote:

Originally Posted by illidari
Hi I was wondering if anyone could explain this to me,

I have

Series (-1)^n n/ln(n)
sum : infinite
n:2

I took the derivative and got : 1/ln(x) - 1/(ln(x)^2)

How do I determine if this is a decreasing or increasing function.

From what I could tell 2 is the only value to make it go <0 , so is this neither increasing or decreasing?

You wrote $\sum\limits^\infty_{n=2}(-1)^n\frac{n}{\ln n}$ . This series diverges since the general term' sequence doesn't converge to zero.
I can't understand what you're trying to derivate and wrt what...

Tonio
• Jul 26th 2010, 04:33 PM
illidari
Yeah that is the series I wrote, I was trying to apply the alternating series test. The 2nd part of the equation, excluding (-1)^n, needs to be decreasing

I took the derivative of it and need to determine if that derivative is <0 .

That is the part I got stuck :/
• Jul 26th 2010, 06:12 PM
tonio
Quote:

Originally Posted by illidari
Yeah that is the series I wrote, I was trying to apply the alternating series test. The 2nd part of the equation, excluding (-1)^n, needs to be decreasing

I took the derivative of it and need to determine if that derivative is <0 .

That is the part I got stuck :/

Are you trying to derivate wrt n, which is a discrete variable?! It can't be done, of course. Besides this the series does
not converge at all, Leibnitz or not.

Tonio