11.4DirectandLimitc omparisontest
comparisontest
iii I
an and Ebn areinfiniteserieswithpositiveterms
liapij
supposethat
EEI É
1 it in is convergent and anen or an n then ean isalso convergent
2 If Ebn is divergent and an bn for all n then Ean isalso divergent
pt F
makesuretostate an o bn so
determine if E hparmingvergentor divergent
Ideals I site intMP it soweneedtoknow if enin si solving use 2e sowhen nes n
s t o and we know in
divergent harmonicseries
by comparisontest eatdiverges
or
EE
poweri nnumerator anddenom
generalrulefor ptest highest
again EE I converses
bycomparisontest
does
Inw to Emigre
then Lahn't
whichis a convergent pseries but he n'a s cat limitcomparisontest
d
Ian I a n'me
it i sottiriesconveraeornotnseriesaiverae
let an uh but he bothare positivewhen n ez
ithint timehe tho i line so
bythelimitcomparisontest Ent converges
youtry Determine if Ei 2h conv or air
eimÉt an.inn.i inmitivemenn
life man
g g g so bythelimitcomptest eitherbothconv or air
since Ek is a geometricserieswith r 112 seriesconverges
E
sobyLCT 2h converges
determineif 25 convergesordiverges
note dominatingparto f numeratori s an andwasin denom
let an to bn
21
an time2ns s
tie
no'w
n I is a divergents eries pseries p 1
sobyLot Tsin diverges
comparisontest
iii I
an and Ebn areinfiniteserieswithpositiveterms
liapij
supposethat
EEI É
1 it in is convergent and anen or an n then ean isalso convergent
2 If Ebn is divergent and an bn for all n then Ean isalso divergent
pt F
makesuretostate an o bn so
determine if E hparmingvergentor divergent
Ideals I site intMP it soweneedtoknow if enin si solving use 2e sowhen nes n
s t o and we know in
divergent harmonicseries
by comparisontest eatdiverges
or
EE
poweri nnumerator anddenom
generalrulefor ptest highest
again EE I converses
bycomparisontest
does
Inw to Emigre
then Lahn't
whichis a convergent pseries but he n'a s cat limitcomparisontest
d
Ian I a n'me
it i sottiriesconveraeornotnseriesaiverae
let an uh but he bothare positivewhen n ez
ithint timehe tho i line so
bythelimitcomparisontest Ent converges
youtry Determine if Ei 2h conv or air
eimÉt an.inn.i inmitivemenn
life man
g g g so bythelimitcomptest eitherbothconv or air
since Ek is a geometricserieswith r 112 seriesconverges
E
sobyLCT 2h converges
determineif 25 convergesordiverges
note dominatingparto f numeratori s an andwasin denom
let an to bn
21
an time2ns s
tie
no'w
n I is a divergents eries pseries p 1
sobyLot Tsin diverges
