- #1
Bazzinga
- 45
- 0
So I have this series:
[tex]\sum^{infinity}_{n=3}(-1)^{n-1}\frac{ln(n)}{n}[/tex]
And I'm trying to use the AST to find out if it converges or not.
First of all, I'm stuck trying to show that ln(n)/n is decreasing...
But then after that. I'm assuming I can compare it with 1/n to show that it diverges absolutely, but converges conditionally (since the limit as n -> infinity of ln(n)/n is 0)
I was just wondering what converging absolutely and conditionally meant? We learned in class that absolute convergence implies convergence, does this mean that if its only conditionally convergent it doesn't converge?
[tex]\sum^{infinity}_{n=3}(-1)^{n-1}\frac{ln(n)}{n}[/tex]
And I'm trying to use the AST to find out if it converges or not.
First of all, I'm stuck trying to show that ln(n)/n is decreasing...
But then after that. I'm assuming I can compare it with 1/n to show that it diverges absolutely, but converges conditionally (since the limit as n -> infinity of ln(n)/n is 0)
I was just wondering what converging absolutely and conditionally meant? We learned in class that absolute convergence implies convergence, does this mean that if its only conditionally convergent it doesn't converge?