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Mathematics
Mathematics
Problem
Let
p
p
p
be a real number. Consider the series
∑
n
=
2
∞
(
−
1
)
n
−
1
(
ln
n
)
p
n
\displaystyle \sum_{n=2}^{\infty} (-1)^{n-1}\frac{(\ln n)^{p}}{n}
n
=
2
∑
∞
(
−
1
)
n
−
1
n
(
ln
n
)
p
. For which values of
p
p
p
does this series converge absolutely? a)
p
≤
−
1
p\le -1
p
≤
−
1
b)
p
<
0
p<0
p
<
0
c)
p
<
−
1
p<-1
p
<
−
1
d)
p
>
−
1
p>-1
p
>
−
1
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