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Mathematics
Problem
The identity
1
(
1
−
x
)
2
=
∑
n
=
0
∞
(
n
+
1
)
x
n
\dfrac{1}{(1-x)^{2}}=\sum_{n=0}^{\infty}(n+1)x^{n}
(
1
−
x
)
2
1
=
∑
n
=
0
∞
(
n
+
1
)
x
n
holds for
∣
x
∣
<
1
|x|<1
∣
x
∣
<
1
. Using the first four non-zero terms of this series, which of the following is the best approximation of
1
(
1
−
1
3
)
2
\dfrac{1}{(1-\frac13)^{2}}
(
1
−
3
1
)
2
1
? a)
2.444
2.444
2.444
b)
2.000
2.000
2.000
c)
2.148
2.148
2.148
d)
2.250
2.250
2.250
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