questions

Proof by Deduction &amp; Exhaustion

Let <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>n be an integer.
Prove that
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>n</mi><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">n(n+1)</annotation></semantics></math>n(n+1)
is even.

Recognises that one of the consecutive integers <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>n and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">n+1</annotation></semantics></math>n+1 must be even.

Concludes that <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">n(n+1)</annotation></semantics></math>n(n+1) is even because its factors include an even integer.

Proof by Deduction & Exhaustion Questions

Year 1

Year 2

Proof

Proof by Deduction & Exhaustion

Proof by Contradiction

Algebra & Functions

Indices & Surds

Quadratics

Simultaneous Equations

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