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Mathematics
Problem
Which of the following alternating series diverges? a)
∑
n
=
1
∞
(
−
1
)
n
+
1
1
n
\displaystyle \sum_{n=1}^{\infty} (-1)^{n+1}\,\frac{1}{\sqrt{n}}
n
=
1
∑
∞
(
−
1
)
n
+
1
n
1
b)
∑
n
=
1
∞
(
−
1
)
n
n
n
+
1
\displaystyle \sum_{n=1}^{\infty} (-1)^{n}\,\frac{n}{n+1}
n
=
1
∑
∞
(
−
1
)
n
n
+
1
n
c)
∑
n
=
1
∞
(
−
1
)
n
+
1
ln
n
n
\displaystyle \sum_{n=1}^{\infty} (-1)^{n+1}\,\frac{\ln n}{n}
n
=
1
∑
∞
(
−
1
)
n
+
1
n
ln
n
d)
∑
n
=
1
∞
(
−
1
)
n
+
1
1
n
\displaystyle \sum_{n=1}^{\infty} (-1)^{n+1}\,\frac{1}{n}
n
=
1
∑
∞
(
−
1
)
n
+
1
n
1
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