Mathematics AA
HL only
Paper 3 · calculator
AHL1.15
AHL1.11
Question 1 · 21 marks
Spec and skills
Spec AHL1.15
Spec AHL1.11
This question investigates sums of the form
S
n
=
∑
r
=
1
n
1
r
(
r
+
1
)
(
r
+
2
)
S_{n} = \displaystyle\sum_{r=1}^{n} \frac{1}{r(r + 1)(r + 2)}
S
n
=
r
=
1
∑
n
r
(
r
+
1
)
(
r
+
2
)
1
and their generalisations.
(a)
Find
S
1
S_{1}
S
1
,
S
2
S_{2}
S
2
and
S
3
S_{3}
S
3
as fractions in their lowest terms.
4 marks
S
1
=
S_1 =
S
1
=
S
2
=
S_2 =
S
2
=
S
3
=
S_3 =
S
3
=