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Mathematics
Mathematics
Problem
Let
S
S
S
be the sum of the alternating harmonic series
∑
k
=
1
∞
(
−
1
)
k
+
1
k
\displaystyle \sum_{k=1}^{\infty} \dfrac{(-1)^{k+1}}{k}
k
=
1
∑
∞
k
(
−
1
)
k
+
1
. If
S
50
S_{50}
S
50
denotes the 50th partial sum, which of the following is the greatest possible value of
∣
S
−
S
50
∣
|S-S_{50}|
∣
S
−
S
50
∣
? a)
2
51
≈
0.0392
\displaystyle \frac{2}{51}\approx 0.0392
51
2
≈
0.0392
b)
1
51
≈
0.0196
\displaystyle \frac{1}{51}\approx 0.0196
51
1
≈
0.0196
c)
1
50
=
0.02
\displaystyle \frac{1}{50}=0.02
50
1
=
0.02
d)
1
102
≈
0.0098
\displaystyle \frac{1}{102}\approx 0.0098
102
1
≈
0.0098
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