3.3.1 The Divergence Test
This allows for you to
quickly rejectsome "trivially divergent"series
by definition, On converges to Swhen the partial sum Sn=, An converges to s
as N ->
00, Sn ->
S
and N-1 ->00 Sn-1 ->
S
an Sn-Sn-1
= ->
S- 5 0
=
Ifa an is the nth partial 0 as
given convergent, sum mustconverge to a -> of then:
if a sequence [An3*=, does not converge too as n- x, the series diverges
ex.
An=
Ginan:hi=n=1 to
E, it diverges
thedivergence testis a "one
way test".
Ittells us aboutwhen i anfo butdoes not
say
abouthis An 0.
=
-
This allows for you to
quickly rejectsome "trivially divergent"series
by definition, On converges to Swhen the partial sum Sn=, An converges to s
as N ->
00, Sn ->
S
and N-1 ->00 Sn-1 ->
S
an Sn-Sn-1
= ->
S- 5 0
=
Ifa an is the nth partial 0 as
given convergent, sum mustconverge to a -> of then:
if a sequence [An3*=, does not converge too as n- x, the series diverges
ex.
An=
Ginan:hi=n=1 to
E, it diverges
thedivergence testis a "one
way test".
Ittells us aboutwhen i anfo butdoes not
say
abouthis An 0.
=
-
