$\displaystyle \sum^ \infty_ {n = 1} \frac{(-1)^n}{ln(n+1)}$
How do I use the Alt series test on this summation? I'm pretty sure that the function is > 0, but I'm not sure if its decreasing.
Well, you can't get a negative number with ln(anything) as long as there are no negatives outside the function, so it is indeed positive. And it is decreasing, because as n increases, the denominator increases, so the values are getting smaller and smaller.
Please state the alternating series test (here is some help: Alternating series test - Wikipedia, the free encyclopedia)
Now look at the previous posts again.
1) $\displaystyle \frac{1}{ln(n+1)}> 0$
2) $\displaystyle \frac{1}{ln(n+1)}$ is decreasing
3) $\displaystyle \lim_{n \rightarrow \infty} \frac{1}{ln(n+1)} = \lim_{n \rightarrow \infty} (n+1)$ = $\displaystyle \infty$
By Alt Series Test, $\displaystyle \sum^ \infty _{n=1} \frac{(-1)^n}{ln(n+1)}$ is divergent.