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Mathematics
Mathematics
Problem
For the series
∑
k
=
1
∞
1
k
3
\displaystyle \sum_{k=1}^{\infty} \dfrac{1}{k^{3}}
k
=
1
∑
∞
k
3
1
, let
R
20
=
S
−
S
20
R_{20}=S-S_{20}
R
20
=
S
−
S
20
denote the remainder after the first
20
20
20
terms. Which of the following values is the best upper bound for
R
20
R_{20}
R
20
? a)
0.00113
0.00113
0.00113
b)
0.00125
0.00125
0.00125
c)
0.00250
0.00250
0.00250
d)
0.000108
0.000108
0.000108
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