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Unformatted text preview: miller (dkrnﬁ45) — HW13 — hamrick M (57395) \ 1
.kﬂ/L This print—out should have 20 questions. \3( «47" W
Muitiplechoice questions may continue on @conditionally converge t .550; ﬂwlii’f ” in“,
the next column or page we ﬁnd all choices Q . CC (I {in{'9
before answering. 3. absoiutely convergent we; 2» "
081 10.0 points 004 10.0 points
M . . . . r“ f ..... ._ ._.‘
g’E—Iiqu Determine Whether the series Determine Whether the series; Art s/(W. 2 2 2 2 2 I \ i3, »
div “ W_~l”w +—m... 0° 5 5m‘“'i’”“
’4'” J 3 4 5 6 7 Z (mun wet
HM??? ' is conditionally convergent, absolutely con— nn2 nlnn w r» HP vergent or divergent. A _
'e r‘ “ converges conditionaily, converges absolutely,
, U 1. series is absolutely convergent 01“ diverges as. g 5%:
e24; sewer: W 59" ‘= "" 2_ series is divergent @eries converges conditionally it.“ e 3:3:
ies is conditionally convergent 2' series diverges
002 10.0 points 3. series converges absolutely
Which one of the following series is conver~ 005 10.0 points gent? (r 7 g m.  1 '2 Determine Whether the series 1 y3+gfvira 00 m5 r
'.l. ) ‘ I 4 to: 7 ‘ 10.0 points MW 00 I r'
0 ‘5" a H . , 77
lg' ("Ugh \Wbetermine if the series ' rug“ 2; 4 + W iékl‘iv—ﬁ j (2;) , MW .53; 00 3 10.0 points V? I 2 (g) “ i?" Determine " her the series It it: I 1 “$2 Lax:
,k. I. '_ 1"." r, (AL
00 RH 33/” converges or diverge . a. Z (“1) m 3 3
11:1 2% i "J \ 1  , Mr ‘1“ er: 1;
. SBI'leS converges ‘ him 1) g __,_i 3
A is absoiutely convergent, conditionally con— M we; \' r. L, d Verge“: of divergent. 2. rice diverges
{ 3: .le If“ ‘ f.‘
' 1. divergent i . W 00'? 10.0 points
Wm... "M i a 1m 1; ’7 ilx‘
7 {a A”: l 1°” (b miller (dkm645) w HW13 ~ hemrick — (57395) 2 To apply the root test to an inﬁnite series
Zn on the value of 5. A m m  1m 
p " nlgrée (an) 10.0 points has to be determined.
Compute p for the series 1 Which one of the following properties does
the series 00 n
7tan"1 n 00 5712 + 2
E _ E : ("mun—w]. "W 371
n——1 . in 11.:1 " ‘~« 1’
‘ {rqu {maxym 5M h ‘? :4 r ~§E
1 ,0 m .2. 3”“ {téwwtw :1 ave' ‘
' M 7 WW"? ‘ ‘ LX * v» 4 ,A @a‘osoluteiy convergent § : " "i"
271' r 5 i
2, = m ‘
'0 7 we? L9 2. divergent
R A .
g 3. conditionally cenvergent "‘
771. {310 10.0 points u 10 ..,_
*g‘ f “3:” {gr}?
7 Which one of the foliowing properties does
—— the series /‘—. “M
‘8‘ °° (—6)“ er» Ere"). “"1 (714:3:
have? " m 3 To apply the ratio test to the inﬁnite series . M (L [97 "
ow ' i
E 65m the Value ,1 bsolutely convergent we“? __ X W
n, ‘ A” 2. conditionaily convergent 1‘ M h L r:
M m r, ' f" 4 a _
A = 11m “41 “‘ (1%: 3.; \
“W00 0% . M «mm "H
3. divergent _ ‘ M wk“ 0 d:
has to be determined 353:5?” W“ ‘n "— f
" 7
011 10 0 points “WW” Compute A for the series me some)? Determine whether the series 0° (___1)n+}. 2% rim—:1 0° 1
2; 371—12
n—l 1, A = is absolutely convergent, conditionally con—
vergent, or divergent. 2 A = ""9 1. divergent 3. A m x a @conditioneﬂy convergent 3. absoluteiy convergent miller (dkmﬁélS) ~ HW13 — hsmrick w (57395) 3 / 1112 10.0 points 4. both of them 1/ 10.0 points Find all integers m > 1 for which both of the inﬁnite series \f Which, if any, of the following statements
are true? A. If line on = 0, then 2 an converges. WWOO 51f 2 an is divergent, then X lanl is divergent. C. The Ratio Test can be used to determine
whether 2 1/713 converges. 1. Conly Z .%n ~.: ’ In.”
2. Aend C only HM 'A 4’0. {3‘4" U3 3
. i ' ._
3. all of them [farm l. i
‘ M . ‘\
Decide Whether the series 4. A oniy iW‘gz"
00 n n m 1 “2 . R"
Z 4 ( n > ’L ’5. none of them
n:1 ’ \/ W
_ \iufdp =,{’“( i ‘A ’
converges or diverges. K _““ 6;. A and B only
1. converges V, o\ ‘03 I" We:
. v” {if B only
\Jx‘ PU
@ diverges
————————————————— 8. B and C only 014 10.0 points Determine which, if any, of the following _ ‘ _ b «1 i {X
series diverge. ,  W Li Wei) W ﬂ {316 10.0 points v 4 , ,
A) n, . QJM l“ W m. Determine which, if any, of the series ‘
()0 4n L 1 new Z (m1)nwl 571 E 2W1,“ (B) W 4 .mwtv __ 2n2+3 em (n + HA i {( vac "Q “envy; 1. '1 H1» . W 1:.
1 neither of theikriwog W ' ) B’ Z (Mun m“ w»
. W ‘ y _
2. B only UM My 1) V” are absolutely convergent.
\ Lie“ k
b\. only I i; M %_ «a 1. A only inf“? l miner (skmeze) — HW13 ~ hamrick m (57395) 4 @her of them A oniy 3. both of them 019 10.0 points
Which of the following properties does the 4° series
B only i (_4)n
m1 (Zn)!
017 10.0 points 7'7"
h ?
Determine Whether the series avg
00 m4 ﬂ 1. divergent
Z (*1) 5m + 4
m: 1 absolutely convergent
is absolutely convergent, conditionally con" 3. conditionally convergent vergent or divergent. 1. absoluteiy convergent 2. éivergent 00 1
(—1)?”1 cos @ conditionally convergent “23:1 373
018 101] points is absoiuteiy convergent, conditionally eon—
vergent or divergent.
:Vhigh, if any, of the following statements are 1. conditionaﬁy convergent
rue.
@ The Root rFest can be used to determine 2 abSOIule convergent
"Sth er the series ‘
3 series is divergent
DO
111 is ’9 ‘4.
Z ( ) it;
kxl 2 ~§~ k 1&1?“ converges or diverges. B. The Ratio Test can be used to deter~ ' J. ‘
mine Whether the series Lwei‘)‘ 3
00 \
E 1 i it. 3‘" d
n2 “i
n a: 1
converges or diverges. W) ﬂute 1. neither of them
2. B only 3. both of them ...
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 Fall '09
 hamrick
 Mathematical Series

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