Representing Series as Power Series
AP Calculus BC · Flashcards · Recall
AP CALCULUS BC · FLASHCARDS
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QUESTION
What is the Maclaurin series for
sin
(
x
)
\text{sin}(x)
sin
(
x
)
?
QUESTION
Identify the power series for
1
1
−
2
x
\frac{1}{1-2x}
1
−
2
x
1
.
QUESTION
What is the power series for
1
1
+
x
\frac{1}{1+x}
1
+
x
1
?
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ANSWER
Sum
=
(
−
1
)
n
x
n
\text{Sum} = (-1)^n x^n
Sum
=
(
−
1
)
n
x
n
for
∣
x
∣
<
1
|x| < 1
∣
x
∣
<
1
. Geometric series with alternating signs from ratio
−
x
-x
−
x
.
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