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Mathematics
Mathematics
Problem
Let
S
=
∑
n
=
2
∞
(
−
1
)
n
ln
n
n
2
.
S=\displaystyle\sum_{n=2}^{\infty} (-1)^{n}\dfrac{\ln n}{n^{2}}.
S
=
n
=
2
∑
∞
(
−
1
)
n
n
2
ln
n
.
Determine the least integer
N
N
N
such that
∣
S
−
S
N
∣
<
5
×
10
−
4
|S-S_N|<5\times10^{-4}
∣
S
−
S
N
∣
<
5
×
1
0
−
4
.
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