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Mathematics
Problem
For a real parameter
p
p
p
, let
a
n
=
n
n
p
+
1
a_n=\dfrac{n}{n^{p}+1}
a
n
=
n
p
+
1
n
. For which values of
p
p
p
does the series
∑
n
=
1
∞
a
n
\displaystyle\sum_{n=1}^{\infty} a_n
n
=
1
∑
∞
a
n
diverge by the
n
n
n
th term test?
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