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Mathematics
Mathematics
Problem
The series
∑
n
=
1
∞
4
n
(
n
+
2
)
\displaystyle\sum_{n=1}^{\infty}\dfrac{4}{n(n+2)}
n
=
1
∑
∞
n
(
n
+
2
)
4
converges to
S
=
3
S=3
S
=
3
. What is the least positive integer
N
N
N
for which
∣
S
−
S
N
∣
<
0.01
|S-S_N|<0.01
∣
S
−
S
N
∣
<
0.01
? a)
400
400
400
b)
399
399
399
c)
398
398
398
d)
199
199
199
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