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