- #1
miglo
- 98
- 0
Homework Statement
[tex]\sum_{n=1}^{\infty}\frac{(-1)^n}{\ln(n+1)}[/tex]
Homework Equations
absolute convergence test
nth term test/divergence test
The Attempt at a Solution
so the absolute convergence test says that if the absolute value of the series converges then the original series converges absolutely
so with the series i have, in absolute value is [tex]\sum_{n=1}^{\infty}\frac{1}{\ln(n+1)}[/tex]
then using the nth term test/divergence test the sequence [itex]a_n=\frac{1}{\ln(n+1)}[/itex] goes to zero as n goes to infinity therefore the series converges, so i have absolute convergence
but my book says that it only converges conditionally, what am i doing wrong? or is the book wrong?