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Mathematics
Problem
The series
∑
n
=
0
∞
(
−
1
)
n
n
+
3
(
n
+
1
)
2
\displaystyle\sum_{n=0}^{\infty}(-1)^n\dfrac{n+3}{(n+1)^2}
n
=
0
∑
∞
(
−
1
)
n
(
n
+
1
)
2
n
+
3
is to be approximated by partial sums. Explain whether the sequence
b
n
=
n
+
3
(
n
+
1
)
2
b_n=\dfrac{n+3}{(n+1)^2}
b
n
=
(
n
+
1
)
2
n
+
3
is eventually decreasing, and state whether the alternating series error bound may be applied.
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