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Mathematics
Mathematics
Problem
The alternating series
∑
n
=
1
∞
(
−
1
)
n
+
1
n
\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n}
n
=
1
∑
∞
n
(
−
1
)
n
+
1
equals
ln
2
\ln 2
ln
2
. What is the least integer
N
N
N
such that the absolute error in approximating
ln
2
\ln 2
ln
2
by the
N
N
N
-term partial sum is less than
0.001
0.001
0.001
? a)
999
999
999
b)
1000
1000
1000
c)
1001
1001
1001
d)
500
500
500
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