Math Pro
about
qns
questions
progress
Question 0521
Sigma Notation
2021 Paper 1 Question 5 Variant
Question
Generate new
(a)
Express
4
x
+
18
(
x
+
4
)
(
x
+
5
)
(
x
+
6
)
\frac{4 x + 18}{(x + 4)(x + 5)(x + 6)}
(
x
+
4
)
(
x
+
5
)
(
x
+
6
)
4
x
+
18
in partial fractions.
[3]
(b)
Hence find, in terms of
n
,
{n,}
n
,
∑
r
=
1
n
4
r
+
18
(
r
+
4
)
(
r
+
5
)
(
r
+
6
)
.
\sum_{r=1}^n \frac{4 r + 18}{(r + 4)(r + 5)(r + 6)}.
r
=
1
∑
n
(
r
+
4
)
(
r
+
5
)
(
r
+
6
)
4
r
+
18
.
[3]
(c)
State the value of
∑
r
=
1
∞
4
r
+
18
(
r
+
4
)
(
r
+
5
)
(
r
+
6
)
.
\sum_{r=1}^\infty \frac{4 r + 18}{(r + 4)(r + 5)(r + 6)}.
r
=
1
∑
∞
(
r
+
4
)
(
r
+
5
)
(
r
+
6
)
4
r
+
18
.
[1]
Answer
Back to top ▲
about
questions
progress