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Math135 Assignment 1

Total marks: 20

Due Friday 8 November 2013

All working must be shown.

Marks will be deducted if answer only is given.

Solutions must be clearly and logically presented- marks will be deducted for
inadequate standard of presentation.

An assignment cover sheet must be attached (obtained near SIBT reception
counter).

1) P. 270 Ex 3.2 question 16 (2 marks)

Questions 1-4 refer to the Precalculus notes on the Portal in Unit
Information

2) P. 270 Ex 3.2 question 28 (2 marks)
3) P. 270 Ex 3.2 question 56 (2 marks)
4) P. 270 Ex 3.2 question 64 (2 marks)

n
Questions 5 -6 use mathematical induction to prove that the formula
is true for all numbers

5)
(3 1)1 4 7 … (3 2)

2
n nn −

+ + + + − = (3 marks)

6) 2 2 2 2 ( 1)(2 1)1 2 3 …
6

n n nn + +
+ + + + = (3 marks)

7) Show that 5 1n − is divisible by 4 for all natural numbers n (3 marks)
8) Prove that 2 2( 1) 2n n+ < for all natural numbers 3n ≥ . (3 marks) first4Q x image1.emf image2.emf