Skip to main content

Back to the full dot-point answer

SingaporeFurther MathsQuick questions

Mathematical Induction, Inequalities and Recurrences

Quick questions on Mathematical induction explained: H2 Further Mathematics

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the structure every proof must show?
Show answer
A complete induction proof has four written parts:
What is a vague conclusion?
Show answer
A mark is reserved for the explicit closing statement naming the base case, the implication, and "by the principle of mathematical induction".
What is q1?
Show answer
State the two things you must establish in a proof by mathematical induction. [2 marks]
What is q2?
Show answer
In proving ∑r=1nr=12n(n+1)\sum_{r=1}^{n} r = \tfrac{1}{2}n(n+1), write the expression for ∑r=1k+1r\sum_{r=1}^{k+1} r using the inductive hypothesis. [2 marks]
What is q3?
Show answer
When proving 7n−17^n - 1 is divisible by 66, how should you write the inductive hypothesis? [1 mark]

Have a question we have not covered?

This dot-point answer is short enough that we have not extracted many short questions yet. Read the full dot-point answer or ask Mo, our study assistant, in the chat for follow ups.

All Further MathsQ&A pages