Parity and evenness proofs

A question is this type if and only if it asks to prove that an expression is always even or odd, or involves proving statements about products/sums of consecutive integers being even.

6 questions · Moderate -1.0

1.01a Proof: structure of mathematical proof and logical steps
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Edexcel P4 2020 October Q1
4 marks Moderate -0.5
  1. Given that \(n\) is an integer, use algebra, to prove by contradiction, that if \(n ^ { 3 }\) is even then \(n\) is even.
OCR MEI C3 Q1
2 marks Easy -1.2
1 Prove that the product of consecutive integers is always even.
OCR H240/01 2018 June Q4
4 marks Moderate -0.8
4 Prove algebraically that \(n ^ { 3 } + 3 n - 1\) is odd for all positive integers \(n\).
Edexcel PMT Mocks Q16
4 marks Easy -1.2
16. Use algebra to prove that the product of any two consecutive odd numbers is an odd number.
OCR MEI C1 2006 January Q1
2 marks Easy -1.2
\(n\) is a positive integer. Show that \(n^2 + n\) is always even. [2]
OCR MEI C1 Q9
2 marks Moderate -0.8
\(n\) is a positive integer. Show that \(n^2 + n\) is always even. [2]