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Mathematics
Problem
Let
f
(
x
)
=
2
x
1
−
4
x
f(x)=\dfrac{2x}{1-4x}
f
(
x
)
=
1
−
4
x
2
x
. Which of the following lists the first four nonzero terms of the Maclaurin series for
f
f
f
? a)
2
x
+
4
x
2
+
8
x
3
+
16
x
4
+
⋯
2x+4x^{2}+8x^{3}+16x^{4}+\cdots
2
x
+
4
x
2
+
8
x
3
+
16
x
4
+
⋯
b)
2
x
+
8
x
2
+
32
x
3
+
128
x
4
+
⋯
2x+8x^{2}+32x^{3}+128x^{4}+\cdots
2
x
+
8
x
2
+
32
x
3
+
128
x
4
+
⋯
c)
2
x
−
8
x
2
+
32
x
3
−
128
x
4
+
⋯
2x-8x^{2}+32x^{3}-128x^{4}+\cdots
2
x
−
8
x
2
+
32
x
3
−
128
x
4
+
⋯
d)
2
x
+
8
x
2
+
16
x
3
+
32
x
4
+
⋯
2x+8x^{2}+16x^{3}+32x^{4}+\cdots
2
x
+
8
x
2
+
16
x
3
+
32
x
4
+
⋯
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