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I\Iatb 1320.001 Quiz 06
Fall 2015
Class ID:
Name
Write your 3 favorite convergence tests for series in the space provided below. Your descrip
tioii should be of the form “Given.., if... then...”
Exairiple: Root Test
Given a series of the form
a,
/[[ < 1, then the series converges absolutely.
if iim /JJ > 1, then the series diverges.
if 1im
11 /‘fJ 1, then the test is inconclusive.
(i) if lim÷
(ii)
(iii)
=
You may dusuribe any of time tests frommi the flow chart except the root test given above.
1. Test:
-ftix cLt
2. Test:
3. Test:
/
// SERIES CONVERGENCE/DIVERGENCE FLOW CHART
TEST FOR DIVERGENCE
Does li,_ a,, = 0?
YES
p-SERIES
Does a = 1/oF, n
NO
verges
1?
YES
NO
H
GEOMETRIC SERIES
Does a = ar”
, > 1?
1
YES
NO
I
1.
ALTERNATING SERIES
Does a,, = (—1)b,, or
0?
= (—1)”’b,,, b,,
b & linb
1
YESHIS b,,÷
=
0? 5YES
-j
TELES COPING SERIES
Do subsequent terms cancel out previous terms in he
sum? May have to use partial fractions, properties
of logat itlun etc to put into appi opi iate foi in
i— YES
—
Does
liniS
YES
S
-
s finite”
NO
TAYLOR SERIES
Does a,
= fC”)(a)
(i
—
YES
a)”?
—‘i Is x in interval of convergence?
YES
NO
1,
Try one or more of the following tests
IsO <a <ba?
COMPARISON TEST
nverges
YES
IsO<b<a?
LIMIT COMPARISON TEST
H
Pick{b,,}. Does lim
c finite & a,,,b,, >0?
INTEGRAL TEST
Does a,, = f(n), f(x) is contin
uous, positive & decreasing on
[a,oo)?
RATIO TEST
Is lim a+i/aI
H
ROOT TEST
Is 1im /i
H
1?
1?
—
YES
H
YES
y
anonverges
Does
f
f(x)di converge?
ft YESNO