Question 1
Prove by mathematical induction that 1 + 4 + 9 + ∙∙∙ +
all
∈
(7 marks)
=
(
)(
)
for
Question 2
(7 marks)
Use the principle of mathematical induction to prove that
4 + 32 + 108 + ⋯ + 4
for all integers
≥ 1.
=
( + 1)
Question 3
Use mathematical induction to prove that
∈
.
(7 marks)
×
+
×
+ ∙∙∙ + (
)(
)
=
for all
Question 4
(7 marks)
Use mathematical induction to prove that
3 × 5 + 6 × 6 + 9 × 7 + ⋯ + 3 ( + 4) =
for all positive integers .
( + 1)(2 + 13)
2