Calculus 2 Quiz
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SEQUENCES & SERIES
Question 1
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The power series
∑
n
=
0
∞
(
−
1
)
n
x
2
n
+
1
2
n
+
1
\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{2n+1}
∑
n
=
0
∞
2
n
+
1
(
−
1
)
n
x
2
n
+
1
represents which of the following functions?
A
arctan
(
x
)
\arctan(x)
arctan
(
x
)
for
∣
x
∣
≤
1
|x| \leq 1
∣
x
∣
≤
1
B
sin
(
x
)
\sin(x)
sin
(
x
)
for all real
x
x
x
C
ln
(
1
+
x
)
\ln(1+x)
ln
(
1
+
x
)
for
−
1
<
x
≤
1
-1 < x \leq 1
−
1
<
x
≤
1
D
1
1
+
x
2
\frac{1}{1+x^2}
1
+
x
2
1
for
∣
x
∣
<
1
|x| < 1
∣
x
∣
<
1
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