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Mathematics
Problem
Let
S
S
S
be the sum of the convergent series
∑
k
=
1
∞
1
k
2
\displaystyle\sum_{k=1}^{\infty}\frac{1}{k^{2}}
k
=
1
∑
∞
k
2
1
. Determine the least integer
N
N
N
such that the partial sum
S
N
S_N
S
N
guarantees
∣
S
−
S
N
∣
<
0.001
|S-S_N|<0.001
∣
S
−
S
N
∣
<
0.001
. a)
N
=
1000
N=1000
N
=
1000
b)
N
=
32
N=32
N
=
32
c)
N
=
1001
N=1001
N
=
1001
d)
N
=
999
N=999
N
=
999
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