<s>
is	O
a	O
divergent	B-Algorithm
series	I-Algorithm
,	O
first	O
considered	O
by	O
Euler	O
,	O
that	O
sums	O
the	O
factorials	O
of	O
the	O
natural	O
numbers	O
with	O
alternating	O
signs	O
.	O
</s>
<s>
This	O
series	O
was	O
first	O
considered	O
by	O
Euler	O
,	O
who	O
applied	O
summability	B-Algorithm
methods	I-Algorithm
to	O
assign	O
a	O
finite	O
value	O
to	O
the	O
series	O
.	O
</s>
<s>
The	O
analytic	B-Algorithm
continuation	I-Algorithm
of	O
to	O
all	O
positive	O
real	O
leads	O
to	O
a	O
convergent	O
integral	O
for	O
the	O
summation	O
:	O
</s>
