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**Unformatted text preview: **MATH 170, SECTION 0], EXAM 3
lb‘iday, November 20th, 2009 Name (PRINT clearly): 0 Do not start the test until instructed to do so.
0 No calculators.
a You will receive full credit only if you show all work and explain all steps. 0 If you run out of space, please ask the instructor for additional sheets of paper. Number the sheets clearly and indicate
the problem that is being solved. Scratch work will not be graded. o The maximum possible score is 150. Point values are indicated on the questions.
0 The time limit is 50 minutes. 0 There are a total of 6 problems. Honor pledge “I pledge on my honor that I have neither given nor received unauthorized aid on this assignment" Sign here: 1. Write 2.1—3.5- as a ratio of integers. [10 points] p-i-__ Qalgg .__ 155' + :35
103’ 9—.— +._, 106 «9+ = 3+ I35"
_____ °° | 'n-{
lo’5 ' Z :03) ‘ 317—! 135'. 't 0m m
2. Find the sum of the series 2 ‘1') ______—._—- (“+3Xnﬂ) (ﬂ 3 “:1 [20 paints]
\ Jr 1 r) i
“+3 h + I. 2_
‘ - 3 * .L _ 3. Test the following series for convergence. [30 points] 9° 211+4 (a) "El "7/2 + x 1 "/3
(b) ’2 ( 1+4) I 1:] 211+?) (a) R n + V L\m|}‘ Q) GAD-">0"
Z 1,: "1’
“'4 Y1, N1
97’} ‘I’ L‘ '4’?- 5‘72.
WW1} m gen 41M
1;. IYYL 11/:—
hﬂw J?” Maw h 4. n
m 7.
an I
16% §6n02 Z- 3.??—
14:4
MOQ 90 2”” comma“ 4. Decide whether the following series converge conditionally, converge absolutely. or diverge. [40 points] (a) ’§1(-1)"-1#. A31 CD 1% 5:: a o,
‘h/HO W1 V 171 Vt kit
@ gh): 97L 1;) [£7X)= #1716“ '26-” 6’ g—E—(’#X)<o
7L ,K'I- X-5
Jemwﬁ '03 A S'T mmgc/r
(B) Mb w m 3L
(ML
_ \
Om” _ Cm“) l x (2m), - "H. O ‘
26“)! ml C2m+2)(ln+t) 5. Consider the inﬁnite series 3 3-5 3-5-7
.1. _ + 3-5-7'9
4 '11-? 4-7-10 4-7-10-13—m (a) Based on the pattern give a formula for the n‘h term of the series. [5 points}
(b) Test, the series for convergence. [15 points] u 9;
3
4‘—
W 93 6. Find the values of p for which the following series converges 2:1! n(n2 + l)”. [30 points] h—voo + “’3‘” M 193 (,omfm'm Come ?WWZ}3 M ”(2{’+‘)>l ...

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