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Mathematics
Problem
Consider the series
∑
n
=
2
∞
n
k
+
5
n
k
+
1
ln
n
.
\sum_{n=2}^{\infty}\frac{n^{k}+5}{n^{k+1}\ln n}.
n
=
2
∑
∞
n
k
+
1
ln
n
n
k
+
5
.
For which real values of
k
k
k
does this series converge? a) It converges if and only if
k
>
0
k>0
k
>
0
. b) It converges for all real
k
k
k
. c) It diverges for all real
k
k
k
. d) It converges if and only if
k
<
−
1
k<-1
k
<
−
1
.
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