Graphics Reference
In-Depth Information
2 For
x
x
x
x
1, let
s
1
...
, a sum of only
n
terms.
By considering
x
·
s
(
x
1)/(
x
1).
Comparethis with qn 1.3(vi). It is also conventional to write
s
s
, provethat
s
,as
defined in the first line, in the form
x
or
x
.
3 By decomposing 1/
r
(
r
1) into partial fractions, or by induction,
provethat
1
1 · 2
1
2 · 3
...
1
n
(
n
1)
1
1
n
1
.
Express this result using the
notation.
1
r
(
r
1)
, provethat (
s
4 If
s
)
1as
n
.
This result is also written
1
r
(
r
1)
1.
When discussing whether the series
a
...
has a sum, we construct the sequence (
s
a
a
...
a
) thus:
s
a
,
s
a
a
,
s
a
a
a
,
...
s
a
a
a
a
...
,
...
and so on.
) is called the
sequence of partial sums
of the series.
When the sequence (
s
The sequence (
s
) is convergent to
s
wesay that
the series is
convergent
to
s
, or has thesum
s
. Symbolically, the series
a
is said to
be
convergent
when
the sequence of partial sums
(
s
), defined by
s
a
is convergent. When (
s
)
s
as
n
, wewrite
a
s
,
and we say that the series has the sum
s
.
