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Unformatted text preview: MA 166 EXAM 3 Spring 2005 Page 1/4 NAME
STUDENT ID
RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, student ID number, recitation instructor’s name and recitation time
in the space provided above. Also write your name at the top of pages 2, 3, and 4. 2. The test has four (4) pages, including this one.
3. Write your answers in the boxes provided. 4. You must show sufﬁcient work to justify all answers. Correct answers with inconsistent
work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes or calculators may be used on this test. (9) 1. Determine whether the following statements are true or false (circle T or (You do
not need to show work for this problem). n——)oo 00
(a) If lim an = 0, then 2 an converges. T F
n=1 00 00
(b) If 0 S an 3 bn for all n 2 1, and Earn diverges, then an diverges. T F n=1 n=1 m _m
(c) If 2 an diverges, then 2 Ian] diverges. T F
n=1 n=1 (9) 2. Determine whether each of the following series is absolutely convergent, conditionally
convergent or divergent. (You do not need to Show work for this problem). ‘” 2“” C:]
“” 2511353”) I: MA 166 Exam 3 Spring 2005 Name ___________________. Page 2/4 (27) 2. Determine whether each series is convergent .or divergent. You must verify that the
conditions of the test are satisﬁed and write your conclusion in the small box. Show all necessary work here : By the test, the series is (b) OD M8
“$13 Show all necessary work here : By the test, the series is MA 166 Exam 3 Spring 2005 Name Page 3/4 (e) Z (4)"? Show all necessary work here : By the test, the series is (12) 4. Find the sum of the series if it is convergent or write “divergent” in the box. No
partial credit. °° 3 —4 n
<a> 2: gm: n=0
(b) 2 (‘55? (—1)”. n! 00
(8) 5. Consider the series 2
n=1 (a) Write out the ﬁrst six terms of the series. (b) Find the smallest number of terms that we need to add in order to estimate the sum of the series with error < 0.01. . MA 166 Exam 3 Spring 2005 Name ______.________._________. Page 4/4 x".
n25” w .
(16) 6. For the power series 2 (—1)" , ﬁnd the following, showing all work.
n=1 (a) The radius of convergence R. (b) The interval of convergence. (Don’t forget to check the end points).
Interval of convergence (10) 7(a). Find the power series representation for (b) Find the power series representation for (Hint: Use part (a) and differenti— 1
(556)” ation) . (9) 8. Find the ﬁrst three nonzero terms of the Taylor series of f = ﬂ centered at a = 4. ...
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 Spring '00
 NA
 Power Series, Mathematical Series, power series representation, necessary work

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