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Question 0521
Sigma Notation
2021 Paper 1 Question 5 Variant
Question
Generate new
(a)
Express
4
x
+
22
(
x
+
4
)
(
x
+
5
)
(
x
+
6
)
\frac{4 x + 22}{(x + 4)(x + 5)(x + 6)}
(
x
+
4
)
(
x
+
5
)
(
x
+
6
)
4
x
+
22
in partial fractions.
[3]
(b)
Hence find, in terms of
n
,
{n,}
n
,
∑
r
=
1
n
4
r
+
22
(
r
+
4
)
(
r
+
5
)
(
r
+
6
)
.
\sum_{r=1}^n \frac{4 r + 22}{(r + 4)(r + 5)(r + 6)}.
r
=
1
∑
n
(
r
+
4
)
(
r
+
5
)
(
r
+
6
)
4
r
+
22
.
[3]
(c)
State the value of
∑
r
=
1
∞
4
r
+
22
(
r
+
4
)
(
r
+
5
)
(
r
+
6
)
.
\sum_{r=1}^\infty \frac{4 r + 22}{(r + 4)(r + 5)(r + 6)}.
r
=
1
∑
∞
(
r
+
4
)
(
r
+
5
)
(
r
+
6
)
4
r
+
22
.
[1]
Answer
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