Question 1

(a) Use mathematical induction to prove that

(b)

n

7

=

Σk(k+1)(k+3) 36

k=1

for all positive integers n.

Use the result in (a) to find the value of

3n+ 7

6(n+1)(n+ 2)(n+3)

100

1

Σ(k+ 1)(k+ 2) (k+4)

k=3

Show all essential working in your calculation.

(10 marks)

(5 marks)