- #1

- 590

- 0

Σ((-1)

^{n-1})*((ln

^{p}(n)))/n) (p>0)

first thing i see here is integration, so i can tell if the series of absolute values converges or not, if it does then i know that my original series must converge.

t=ln(n)

dt=dn/n

so i have an integral from 0 to infinity of

t

^{p}dt

which is a simple integration and i find that the absolute values' series diverges which tells me that my series may conditionally converge if

lim a

_{n}=0 (which it is)

and a

_{n}>a

_{(n+1)}which it is not since the series keeps on rising in its absolute value, because of "p".

so how do i prove that the series converges?