<s>
Grandi	O
's	O
series	O
is	O
just	O
one	O
example	O
of	O
a	O
divergent	B-Algorithm
geometric	I-Algorithm
series	I-Algorithm
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
if	O
one	O
uses	O
stronger	O
methods	O
of	O
summability	O
,	O
then	O
the	O
Dirichlet	O
series	O
for	O
η	O
defines	O
a	O
function	O
on	O
the	O
whole	O
complex	O
plane	O
—	O
the	O
Dirichlet	O
eta	O
function	O
—	O
and	O
moreover	O
,	O
this	O
function	O
is	O
analytic	B-Language
.	O
</s>
<s>
Since	O
η(z )	O
and	O
(	O
121−z	O
)	O
are	O
both	O
analytic	B-Language
on	O
the	O
entire	O
plane	O
and	O
the	O
latter	O
function	O
's	O
only	O
zero	O
is	O
a	O
simple	O
zero	O
at	O
z	O
=	O
1	O
,	O
it	O
follows	O
that	O
ζ(z )	O
is	O
meromorphic	O
with	O
only	O
a	O
simple	O
pole	O
at	O
z	O
=	O
1	O
.	O
</s>
