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Which of the following are power series (select all that apply)?
Related Topics
Wize University Calculus 2 Textbook > Power Series
Power Series
4 Activities
Which of the following are power series (select all that apply)?
y
(
x
)
=
∑
n
=
0
∞
2
n
+
1
n
!
x
2
n
−
1
y(x) = \sum_{n=0}^{\infty}\limits \frac{2n+1}{n!}x^{2n-1}
y
(
x
)
=
n
=
0
∑
∞
n
!
2
n
+
1
x
2
n
−
1
f
(
x
)
=
2
+
x
f(x) = 2 + x
f
(
x
)
=
2
+
x
y
(
x
)
=
∑
n
=
−
5
∞
1
(
n
+
10
)
!
x
2
n
+
10
y(x) = \sum_{n=-5}^{\infty}\limits \frac{1}{(n+10)!}x^{2n+10}
y
(
x
)
=
n
=
−
5
∑
∞
(
n
+
10
)!
1
x
2
n
+
10
g
(
x
)
=
∑
k
=
2
7
2
n
x
2
n
+
1
g(x) = \sum_{k=2}^{7}\limits \frac{2}{n} x^{2n+1}
g
(
x
)
=
k
=
2
∑
7
n
2
x
2
n
+
1
f
(
x
)
=
ln
(
2
)
+
∑
j
=
1
∞
sin
(
j
)
(
x
−
j
)
j
f(x) = \ln(2) + \sum_{j = 1}^{\infty}\limits \sin(j)(x-j)^j
f
(
x
)
=
ln
(
2
)
+
j
=
1
∑
∞
sin
(
j
)
(
x
−
j
)
j
h
(
x
)
=
ln
(
2
)
+
∑
j
=
1
∞
sin
(
j
)
(
x
−
π
)
j
h(x) = \ln(2) + \sum_{j = 1}^{\infty}\limits \sin(j)(x-\pi)^j
h
(
x
)
=
ln
(
2
)
+
j
=
1
∑
∞
sin
(
j
)
(
x
−
π
)
j
a
(
x
)
=
2
x
2
−
2
x
+
2
−
2
x
+
2
x
2
−
2
x
3
+
2
x
4
∓
…
a(x) = \frac{2}{x^2} - \frac{2}{x} + 2 - 2x + 2x^2 - 2x^3 + 2x^4 \mp \, \dots
a
(
x
)
=
x
2
2
−
x
2
+
2
−
2
x
+
2
x
2
−
2
x
3
+
2
x
4
∓
…
I don't know
Check Submission
More Power Series Questions:
Power Series
For what values of ‘x’ does the series
∑
n
=
1
∞
(
x
−
2
)
n
3
n
.
n
3
\sum_{n=1}^{\infty}\frac{\left(x-2\right)^n}{3^n.n^3}
∑
n
=
1
∞
3
n
.
n
3
(
x
−
2
)
n
converge?