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Mathematics
Mathematics
Problem
Which of the following infinite series is conditionally convergent? a)
∑
n
=
1
∞
(
−
1
)
n
+
1
n
2
\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n^{2}}
n
=
1
∑
∞
n
2
(
−
1
)
n
+
1
b)
∑
n
=
1
∞
1
n
\displaystyle\sum_{n=1}^{\infty}\frac{1}{n}
n
=
1
∑
∞
n
1
c)
∑
n
=
1
∞
(
−
1
)
n
+
1
n
\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n}
n
=
1
∑
∞
n
(
−
1
)
n
+
1
d)
∑
n
=
1
∞
(
−
1
)
n
+
1
2
n
\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{2^{\,n}}
n
=
1
∑
∞
2
n
(
−
1
)
n
+
1
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