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Mathematics
Mathematics
Problem
The power series for
ln
(
1
+
x
)
\ln(1+x)
ln
(
1
+
x
)
about
x
=
0
x=0
x
=
0
is
∑
n
=
1
∞
(
−
1
)
n
+
1
x
n
n
\displaystyle \sum_{n=1}^{\infty}(-1)^{n+1}\dfrac{x^{n}}{n}
n
=
1
∑
∞
(
−
1
)
n
+
1
n
x
n
for
∣
x
∣
<
1
|x|<1
∣
x
∣
<
1
. Obtain a power-series representation for
1
1
+
x
\dfrac{1}{1+x}
1
+
x
1
and give its general term.
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