<s>
is	O
divergent	B-Algorithm
if	O
and	O
only	O
if	O
|r|≥1	O
.	O
</s>
<s>
This	O
is	O
true	O
of	O
any	O
summation	B-Algorithm
method	I-Algorithm
that	O
possesses	O
the	O
properties	O
of	O
regularity	O
,	O
linearity	O
,	O
and	O
stability	O
.	O
</s>
<s>
It	O
is	O
useful	O
to	O
figure	O
out	O
which	O
summation	B-Algorithm
methods	I-Algorithm
produce	O
the	O
geometric	O
series	O
formula	O
for	O
which	O
common	O
ratios	O
.	O
</s>
<s>
One	O
application	O
for	O
this	O
information	O
is	O
the	O
so-called	O
Borel-Okada	B-Algorithm
principle	I-Algorithm
:	O
If	O
a	O
regular	O
summation	B-Algorithm
method	I-Algorithm
sums	O
Σzn	O
to	O
1/	O
( 1	O
-	O
z	O
)	O
for	O
all	O
z	O
in	O
a	O
subset	O
S	O
of	O
the	O
complex	O
plane	O
,	O
given	O
certain	O
restrictions	O
on	O
S	O
,	O
then	O
the	O
method	O
also	O
gives	O
the	O
analytic	B-Algorithm
continuation	I-Algorithm
of	O
any	O
other	O
function	O
on	O
the	O
intersection	O
of	O
S	O
with	O
the	O
Mittag-Leffler	O
star	O
for	O
f	O
.	O
</s>
