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Mathematics
Problem
For
∣
x
∣
<
1
|x|<1
∣
x
∣
<
1
, which of the following series equals
f
(
x
)
=
x
1
+
x
3
\displaystyle f(x)=\dfrac{x}{1+x^{3}}
f
(
x
)
=
1
+
x
3
x
? a)
∑
n
=
0
∞
x
3
n
+
1
\displaystyle \sum_{n=0}^{\infty}x^{3n+1}
n
=
0
∑
∞
x
3
n
+
1
b)
∑
n
=
0
∞
(
−
1
)
n
x
3
n
\displaystyle \sum_{n=0}^{\infty}(-1)^n x^{3n}
n
=
0
∑
∞
(
−
1
)
n
x
3
n
c)
∑
n
=
0
∞
(
−
1
)
n
x
3
n
+
1
\displaystyle \sum_{n=0}^{\infty}(-1)^n x^{3n+1}
n
=
0
∑
∞
(
−
1
)
n
x
3
n
+
1
d)
∑
n
=
0
∞
(
−
1
)
n
x
n
+
1
\displaystyle \sum_{n=0}^{\infty}(-1)^n x^{n+1}
n
=
0
∑
∞
(
−
1
)
n
x
n
+
1
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