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Mathematics
Problem
Consider the tail
R
N
=
∑
n
=
N
+
1
∞
1
n
2
R_N=\displaystyle\sum_{n=N+1}^{\infty}\frac1{n^{2}}
R
N
=
n
=
N
+
1
∑
∞
n
2
1
, where
N
N
N
is a positive integer. Which of the following values of
N
N
N
is the smallest that guarantees
R
N
<
0.0005
R_N<0.0005
R
N
<
0.0005
? a)
2000
2000
2000
b)
2500
2500
2500
c)
2001
2001
2001
d)
1999
1999
1999
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