More Series
What about an arithmetic series?
For a series to be convergent, we must have lim
n
→∞
a
n
= 0
(Just remember that this is required but not sufficient to ensure convergence)
The second famous type of series we will work with are called
telescoping series
.
If
a
n
=
c
n

c
n
+1
, then what does
b
n
look like?
So if
c
n
is a convergent sequence, then
∞
X
n
=1
a
n
is a convergent series.
In general, just write out the general
n
th
partial sum and cancel as many terms as possible.