Alternating Series Test Reference
$$ \sum_{i=0}^\infty \frac{(-1)^n}{n} $$
This alternating series fails the p-series test because the exponent of n = 1.
Yet it seems to pass the alternating series test.
1 - $a_n$ must be positive. True.
2 - Terms must be decreasing. $\frac{d}{dn} 1/n = -n^{-2}$, which is < 1. True.
3 - $ \lim_{n\rightarrow\infty} 1/n = 0 $ True.
$(-1)^n/n$ is clearly a divergent series, so why does it pass the AST?