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Mathematics
Problem
Let
S
N
=
∑
n
=
0
N
(
−
1
)
n
0.6
2
n
+
1
2
n
+
1
S_N = \displaystyle \sum_{n=0}^{N}(-1)^n\frac{0.6^{2n+1}}{2n+1}
S
N
=
n
=
0
∑
N
(
−
1
)
n
2
n
+
1
0.
6
2
n
+
1
be the
N
N
N
th partial sum of the series for
arctan
(
0.6
)
\arctan(0.6)
arctan
(
0.6
)
. What is the least value of
N
N
N
for which
∣
arctan
(
0.6
)
−
S
N
∣
<
10
−
5
|\arctan(0.6)-S_N|<10^{-5}
∣
arctan
(
0.6
)
−
S
N
∣
<
1
0
−
5
? a)
N
=
8
N=8
N
=
8
b)
N
=
7
N=7
N
=
7
c)
N
=
6
N=6
N
=
6
d)
N
=
9
N=9
N
=
9
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