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Math 227 Sections 4 and 5
Written HW 12 due Friday 4/22
Some exercises and applications with power series
1. Start with the geometric series
1
1
x
=
1
X
n
=0
x
n
(valid for
1
< x <
1
).
f
(
x
) =
1
(1
x
)
2
:
(b) Test your answer by substituting in the value
x
= 0
:
1
terms. The sum should be fairly close to
1
=
(1
&
0
:
1)
2
= 1
:
234 567 901
:
(c) Try the same thing using
x
= 0
:
5
:
approximation of
1
=
(1
&
0
:
5)
2
= 4
:
00000
:
What is the reason for this? (Look at the terms you are
of the series you are omitting.)
20
terms of the series using
x
= 0
:
5
:
Answer:
3
:
999 958 038
.
2. Replace
x
by
x
in your series for
f
(
x
)
to obtain a series for
g
(
x
) =
1
(1+
x
)
2
:
The next exercise uses
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 Spring '09
 CHEUNG
 Calculus, Geometric Series, Power Series

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