Proof by Mathematical Induction

ME-P1 is worth about 3 marks out of 100 in recent HSC Mathematics Extension 1 papers. Practise 4 exam-style questions (short answer, multiple choice) with instant marking and a worked solution for every question.

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Example questions

Example 1 · 1 mark · multiple choice

In proving $2^{n} > n$ for all integers $n \geq 1$ by induction, what must be shown in the inductive step?

AIf $2^{k + 1} > k + 1$ , then $2^{k} > k$
BIf $2^{k} > k$ , then $2^{k + 1} > k + 1$
C $2^{k} > k$ for all $k$
D $2^{1} > 1$

Example 2 · 3 marks · short answer

Use mathematical induction to prove that $1 + 3 + 5 + \dots + (2 n - 1) = n^{2}$ for all integers $n \geq 1$ .

Example 3 · 4 marks · short answer

Use mathematical induction to prove that $\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \dots + \frac{1}{n ( n + 1 )} = \frac{n}{n + 1}$ for all integers $n \geq 1$ .

Answers and worked solutions appear when you practise these questions.

Proof by Mathematical Induction

Example questions

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