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Mathematics
Mathematics
Problem
Three series are given. I.
∑
n
=
1
∞
n
2
n
2
+
1
\displaystyle \sum_{n=1}^{\infty}\frac{n^{2}}{n^{2}+1}
n
=
1
∑
∞
n
2
+
1
n
2
II.
∑
n
=
1
∞
(
−
1
)
n
n
\displaystyle \sum_{n=1}^{\infty}\frac{(-1)^{n}}{\sqrt{n}}
n
=
1
∑
∞
n
(
−
1
)
n
III.
∑
n
=
1
∞
2
n
n
+
1
\displaystyle \sum_{n=1}^{\infty}\frac{2n}{n+1}
n
=
1
∑
∞
n
+
1
2
n
Which of the series diverge based on the behavior of their
n
n
n
th terms? a) III only b) I only c) I and III only d) I, II, and III
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