2013澳大利亚高考数学试题答案(11)

Question 14 (15 marks) Use a SEPARATE writing booklet.

(a) The diagram shows the graph y = ln x.

= ln x

By comparing relevant areas in the diagram, or otherwise, show that

lnt > 2 t 1 t + 1

, for t > 1.(b) Let z i

2 = 1 + i and, for n > 2, let z n= z n 1 1 + z

n 1

. Use mathematical induction to prove that zn = n for all integers n ≥ 2.

Question 14 continues on page 13

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