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133_hw10.pdf
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Math 133
HW 10: due Friday, December 1 in class
Be sure to show your work!
1. Use your knowledge of geometric series to find the interval of convergence of each series below,
as well as an expression for the sum as a function of x.
(a)
∞
X
(x + 1)2n
9n
n=0
1
(−4, 2)
(b)
∞
X
1−
(x+1)2
9
(ex − 4)n
n=0
1
1−(ex −4)
(ln 3, ln 5)
2. Find the center, radius of convergence, and interval of convergence of each power series.
(a)
∞
X
n(x + 3)n
5n
n=0
(b)
−3
∞
X
n=0
(c)
(d)
(−8, 2)
x2n
4n (n2 + n + 1)
0
2
[−2, 2]
∞
n
X (2x − 1)
n=1
1
2
∞
X
n=0
(e)
5
n · 3n
3
2
n!(x −
2n
1
P∞
n=0
[−1, 2)
1)n
0
{1}
(x−2)n
n! 5n
2
∞
(−∞, ∞)
n
∞
X
n+1
(f)
xn
n
n=0
0
1
(−1, 1)
1
…
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