What happens when the series is alternating and the tests that I know are inconclusive?
$\sum_{n=1}^\infty (-1)^n (n/(n+5))$.
The $b_n$ series is not decreasing, so I can't use the alternating series test (I took the derivative of $f(x)=x/(x+5)$ - slope is positive everywhere).
When I do the ratio test I get $=1$, so inconclusive.
So - am I allowed to simply ignore the alternating portion of the series and apply the divergence test which allows me to say lim as $n$ goes to $\infty$ of $a_n=1$ and since the limit does NOT $=0$, then the series diverges?
I thought I could only use the divergence test on non-alternating series!