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Mathematics
Problem
The power series
∑
n
=
0
∞
(
−
1
)
n
x
2
n
+
1
2
n
+
1
\displaystyle \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{2n+1}
n
=
0
∑
∞
2
n
+
1
(
−
1
)
n
x
2
n
+
1
converges for
∣
x
∣
<
1
|x|<1
∣
x
∣
<
1
. Determine the elementary function to which this series converges on that interval.
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