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