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Question 0501c
Sigma Notation
Method of Differences III
Question
Generate new
Given that
f
(
0
)
=
5
,
{f(0)=5,}
f
(
0
)
=
5
,
f
(
1
)
=
3
{f(1)=3}
f
(
1
)
=
3
and
f
(
2
)
=
3
,
{f(2)=3,}
f
(
2
)
=
3
,
express
∑
r
=
1
n
(
2
u
r
+
1
−
3
u
r
+
u
r
−
1
)
\sum_{r=1}^n \Big( 2 u_{r+1} - 3 u_r + u_{r-1} \Big)
r
=
1
∑
n
(
2
u
r
+
1
−
3
u
r
+
u
r
−
1
)
in the form
a
+
b
u
n
+
c
u
n
+
1
,
a + bu_n + cu_{n+1},
a
+
b
u
n
+
c
u
n
+
1
,
where
a
,
b
{a, b}
a
,
b
and
c
{c}
c
are constants.
Attempt
a
=
{a=}
a
=
b
=
{b=}
b
=
c
=
{c=}
c
=
Answer
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