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Question 0501c
Sigma Notation
Method of Differences III
Question
Generate new
Given that
f
(
0
)
=
3
,
{f(0)=3,}
f
(
0
)
=
3
,
f
(
1
)
=
5
{f(1)=5}
f
(
1
)
=
5
and
f
(
2
)
=
9
,
{f(2)=9,}
f
(
2
)
=
9
,
express
∑
r
=
1
n
(
f
(
r
−
1
)
−
2
f
(
r
)
+
f
(
r
+
1
)
)
\sum_{r=1}^n \Big( f(r-1) - 2 f(r) + f(r+1) \Big)
r
=
1
∑
n
(
f
(
r
−
1
)
−
2
f
(
r
)
+
f
(
r
+
1
)
)
in the form
a
+
b
f
(
n
)
+
c
f
(
n
+
1
)
,
a + bf(n) + cf(n+1),
a
+
b
f
(
n
)
+
c
f
(
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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