<s>
In	O
mathematics	O
,	O
the	B-Algorithm
Weierstrass	I-Algorithm
M-test	I-Algorithm
is	O
a	O
test	O
for	O
determining	O
whether	O
an	O
infinite	O
series	O
of	O
functions	O
converges	B-Algorithm
uniformly	I-Algorithm
and	O
absolutely	O
.	O
</s>
<s>
Weierstrass	B-Algorithm
M-test	I-Algorithm
.	O
</s>
<s>
converges	O
absolutely	O
and	O
uniformly	B-Algorithm
on	O
A	O
.	O
</s>
<s>
The	O
result	O
is	O
often	O
used	O
in	O
combination	O
with	O
the	O
uniform	B-Algorithm
limit	I-Algorithm
theorem	I-Algorithm
.	O
</s>
<s>
Since	O
N	O
does	O
not	O
depend	O
on	O
x	O
,	O
this	O
means	O
that	O
the	O
sequence	O
of	O
partial	O
sums	O
converges	B-Algorithm
uniformly	I-Algorithm
to	O
the	O
function	O
S	O
.	O
Hence	O
,	O
by	O
definition	O
,	O
the	O
series	O
converges	B-Algorithm
uniformly	I-Algorithm
.	O
</s>
<s>
Analogously	O
,	O
one	O
can	O
prove	O
that	O
converges	B-Algorithm
uniformly	I-Algorithm
.	O
</s>
