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Unformatted text preview: MA 166 EXAM 3 Spring 2002 Page 1/4 D 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. ’ (15) 1. Circle the letter of the correct response. (You need not show work for this problem). 00
(a) Which of the following statements are always true for any series 21 an with
71,: ‘positive terms? (I) If lim an 2 0, then 020 an converges. n——)oo n=l
. 1 0°
(II) If ﬁlingo Man —— 5, then "Elan converges.
00
(III) If lim 9,1 = ~53, then 2 an diverges.
11,—)00 W 6 n=1 (IV) If lim “"+1 z 1, then °2° an diverges.
nmo an n=1 A. (II) and (IV) only B. (I), (II) and (III) only C. (I) and (III) only
D. (II) and (III) only E. all (b) Which of the following series converge? (I) 2 71m (II) 2; (n— 1)2n n=1 A. (I) and (II) only B. (I) and (III) only C. (II) and (III) only D. (III) only '
E. all MA 166 Exam 3 Spring 2002 Name _____—_ Page 2/4 ’ (20) 2. Determine whether each series is convergent or divergent. You must Show all necessary
work and write your conclusion in the small box. °° 1
(a) :4; s/nm + 1)(n + 2) Show all necessary work here: Show all necessary work here: ’ By the test, the series is MA 166 Exam 3 Spring 2002 Name ____________ Page 3/4 (—1)"1_ CXJ
’ (10) 3. Consider the convergent alternating series Z N. n=1
(a) Write out the ﬁrst sixterms 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. 00
_1 71—1
(10) 4. Determine whether the series 2 ; is absolutely convergent, conditionally "=1 nﬁ convergent, or divergent. You must justify your answer. Q (9) 5. Find the sum of each series if it is convergent, or write divergent in the box. No partial
credit. (3) 2 6—211, n=1 VCJ
Sage)" +1 I ~ :1
E ' (C) an—l
n=1 MA 166 Exam 3 Spring 2002 Name —_____ Page 4/4 00 ’ (16) 6. Find the interval of convergence of the power series Zn3(x — 5)”. Don’t forget to 71:1
test for convergence at the end points of the interval. You mustshow all work. 1 (10) 7. Evaluate the indeﬁnite integral / d3: as a power series and determine its radius 1+x4 . of convergence R. (10) 8. Find the Taylor series for f = :5;— centered at a = 1. ...
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 Calculus, Mathematical Series, student id, recitation instructor, Recitation Time

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