Originally Posted by

**wyhwang7** hello, so i'm reviewing the chapter on absolute and conditional divergence, and this chapter has me completely baffled.

are p-series not always applicable?

because, for example,

infinite

sigma [(-1)^n]/(n)^1/2

n=1

ace of n = 1/n^(1/2)

converges, even though p=1/2 < 1.

but at the same time,

infinite

sigma 1/n^(1/2)

n=1

is divergent because the p-series somehow applies to this one and not that one.

are p-series only applicable for non-alternating series? when does the leibniz rule override the p-series rule?