<s>
This	O
convergence	B-Algorithm
problem	I-Algorithm
for	O
continued	O
fractions	O
is	O
inherently	O
more	O
difficult	O
than	O
the	O
corresponding	O
convergence	B-Algorithm
problem	I-Algorithm
for	O
infinite	O
series	O
.	O
</s>
<s>
The	O
convergence	B-Algorithm
problem	I-Algorithm
is	O
much	O
more	O
difficult	O
when	O
the	O
elements	O
of	O
the	O
continued	O
fraction	O
are	O
complex	O
numbers	O
.	O
</s>
<s>
Because	O
the	O
proof	O
of	O
Worpitzky	O
's	O
theorem	O
employs	O
Euler	O
's	O
continued	O
fraction	O
formula	O
to	O
construct	O
an	O
infinite	O
series	O
that	O
is	O
equivalent	O
to	O
the	O
continued	O
fraction	O
x	O
,	O
and	O
the	O
series	O
so	O
constructed	O
is	O
absolutely	O
convergent	O
,	O
the	B-Algorithm
Weierstrass	I-Algorithm
M-test	I-Algorithm
can	O
be	O
applied	O
to	O
a	O
modified	O
version	O
of	O
x	O
.	O
</s>
