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
=
3
n
1
(
r
+
1
)
(
r
+
3
)
=
9
40
−
1
2
n
+
4
−
1
2
n
+
6
.
\sum_{r=3}^n \frac{1}{(r + 1) (r + 3)} = \frac{9}{40} - \frac{ 1 }{ 2 n + 4 } - \frac{ 1 }{ 2 n + 6 }.
r
=
3
∑
n
(
r
+
1
)
(
r
+
3
)
1
=
40
9
−
2
n
+
4
1
−
2
n
+
6
1
.
[4]
(b)
Explain why
∑
r
=
3
∞
1
(
r
+
1
)
(
r
+
3
)
{\displaystyle \sum_{r=3}^\infty \frac{1}{(r + 1) (r + 3)}}
r
=
3
∑
∞
(
r
+
1
)
(
r
+
3
)
1
is a convergent series, and state the value of the sum to infinity.
[2]
Answer
Back to top ▲
about
questions
progress