ii 5 Alternatings eriesTest
consider
c
th alternatesbetweenpos negterms
alternatingseriestest
it Eun ba bi be ba ba t determine if E h convergesor diverges
If Iftp.ltingm
weseethat bn in n't one or denomgetslargers osequencedear
a him aim.tn O
I it
thentheseriesconverges
Inima
so denominatorg etslargersobnisdecreasing
himanima o sobyAst series converges
iii in
iiiiitiiai.am
1h 1msend2x to
divergeson
Ast Ee no m converges
Eltis a convergent or
o decreasingmen
m
sotheAstisinconclusive
note
gigi in ah him himEh time
youtrust
t.it i ii i ma amrse
c onaratanin
IE i iii i iammnum
bythedivergencetest theseriesdiverges
it's Ean is absolutely convergent it Elant isconvergent
Econ toconvordive theorem if an isabsolutelyconvergent
thenit is convergent
Elani Ehe notethatoppositeisn'ttrue
z
iI I l in tiswhichis
EE i
convergent
ine convergent out E.tn divergent
consider
c
th alternatesbetweenpos negterms
alternatingseriestest
it Eun ba bi be ba ba t determine if E h convergesor diverges
If Iftp.ltingm
weseethat bn in n't one or denomgetslargers osequencedear
a him aim.tn O
I it
thentheseriesconverges
Inima
so denominatorg etslargersobnisdecreasing
himanima o sobyAst series converges
iii in
iiiiitiiai.am
1h 1msend2x to
divergeson
Ast Ee no m converges
Eltis a convergent or
o decreasingmen
m
sotheAstisinconclusive
note
gigi in ah him himEh time
youtrust
t.it i ii i ma amrse
c onaratanin
IE i iii i iammnum
bythedivergencetest theseriesdiverges
it's Ean is absolutely convergent it Elant isconvergent
Econ toconvordive theorem if an isabsolutelyconvergent
thenit is convergent
Elani Ehe notethatoppositeisn'ttrue
z
iI I l in tiswhichis
EE i
convergent
ine convergent out E.tn divergent
