Math Pro
about
qns
questions
progress
Question 0510
Sigma Notation
2010 Paper 2 Question 2 Variant
Question
Generate new
(a)
Prove by the method of differences that
∑
r
=
1
n
1
(
r
+
2
)
(
r
+
4
)
=
7
24
−
1
2
n
+
6
−
1
2
n
+
8
.
\sum_{r=1}^n \frac{1}{(r + 2) (r + 4)} = \frac{7}{24} - \frac{ 1 }{ 2 n + 6 } - \frac{ 1 }{ 2 n + 8 }.
r
=
1
∑
n
(
r
+
2
)
(
r
+
4
)
1
=
24
7
−
2
n
+
6
1
−
2
n
+
8
1
.
[4]
(b)
Explain why
∑
r
=
1
∞
1
(
r
+
2
)
(
r
+
4
)
{\displaystyle \sum_{r=1}^\infty \frac{1}{(r + 2) (r + 4)}}
r
=
1
∑
∞
(
r
+
2
)
(
r
+
4
)
1
is a convergent series, and state the value of the sum to infinity.
[2]
Answer
Back to top ▲
about
questions
progress