Practice Problems for Math 133 Exam 4
Exam 4 will cover the material done in class and in homework from Sections 11.2 – 11.10 plus Sections
10.4 and 10.5. The problems on this sheet should help to remind you of this material. You should also go
through your class notes and your HW problems. It is also especially helpful to go through your quizzes and
check your answers against the solutions posted on the class web page.
1. Find the sum of the series
S
=
∞
X
n
=1
π
n
4
n
and the series
S
=
∞
X
n
=1
3
7
n

1
√
2
n
.
2. Use the Integral Test (IT), Limit Comparison Test (LCT), Comparison Test (CT), Ratio Test (RT)
or the Alternating Series Test (AST) to determine whether the following series converge absolutely,
converge conditionally, or diverge. Show your reasoning clearly and state the test you use.
(a)
S
=
∞
X
n
=1
1
1 +
n
2
(b)
S
=
∞
X
n
=1
3
n
n
!
2
n
!
(c)
S
=
∞
X
n
=1
n
2
+ 5
n
3
n
3

14
n
2
+ 3
(d)
S
=
∞
X
n
=1
π
n
n
(
n
+ 1)
(e)
S
=
∞
X
n
=1
(

1)
n
1
√
n
(f)
S
=
∞
X
n
=1
ln
n
n
2
(g)
S
=
∞
X
n
=1
(

1)
n
n
6
2
n
(h)
S
=
∞
X
n
=1
sin
n
n
3
/
2
3. Find the interval of convergence for the following power series (do not test for convergence at the
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 Spring '07
 Wei
 Math, Taylor Series, Mathematical Series, Web page, n=1, class web page

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