Let
{
š
š
}
š
=
1
ā
{a
n
ā
}
n=1
ā
ā
be a sequence of positive numbers such that:
š
1
ā„
š
2
ā„
š
3
ā„
āÆ
ā„
š
š
ā„
š
š
+
1
ā„
āÆ
a
1
ā
ā„a
2
ā
ā„a
3
ā
ā„āÆā„a
n
ā
ā„a
n+1
ā
ā„āÆ (i.e., the sequence is non-increasing).
lim
ā”
š
ā
ā
š
š
=
0.
lim
nāā
ā
a
n
ā
=0.
Then the alternating series
ā
š
=
1
ā
(
ā
1
)
š
+
1
š
š
ā
n=1
ā
ā
(ā1)
n+1
a
n
ā
is convergent.
Mathbot Says...
I wasn't able to parse your question, but the HE.NET team is hard at work making me smarter.