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Question 0521
Sigma Notation
2021 Paper 1 Question 5 Variant
Question
Generate new
(a)
Express
x
−
2
x
(
x
+
1
)
(
x
+
2
)
\frac{x - 2}{x(x + 1)(x + 2)}
x
(
x
+
1
)
(
x
+
2
)
x
−
2
in partial fractions.
[3]
(b)
Hence find, in terms of
n
,
{n,}
n
,
∑
r
=
1
n
r
−
2
r
(
r
+
1
)
(
r
+
2
)
.
\sum_{r=1}^n \frac{r - 2}{r(r + 1)(r + 2)}.
r
=
1
∑
n
r
(
r
+
1
)
(
r
+
2
)
r
−
2
.
[3]
(c)
State the value of
∑
r
=
1
∞
r
−
2
r
(
r
+
1
)
(
r
+
2
)
.
\sum_{r=1}^\infty \frac{r - 2}{r(r + 1)(r + 2)}.
r
=
1
∑
∞
r
(
r
+
1
)
(
r
+
2
)
r
−
2
.
[1]
Answer
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