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Mathematics Extension 1

Stage 6 · HSC questions by topic

About this subject

Mathematics Extension 1

Atlas organises human-reviewed questions against the NSW Stage 6 Mathematics Extension 1syllabus. Every published question retains its exam source and page.

Syllabus: NESA Stage 6 (2017)
Explore the NESA Stage 6 (2017) syllabus topics

Functions

  • Further Work with Functions
  • Polynomials

Trigonometric Functions

  • Inverse Trigonometric Functions
  • Further Trigonometric Identities
  • Trigonometric Equations

Calculus

  • Rates of Change
  • Further Calculus Skills
  • Applications of Calculus

Combinatorics

  • Working with Combinatorics

Proof

  • Proof by Mathematical Induction

Vectors

  • Introduction to Vectors

Statistical Analysis

  • The Binomial Distribution
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2023HSC
Q12 (b)

Use mathematical induction to prove that

(1×2)+(2×22)+(3×23)+⋯+(n×2n)=2+(n−1)2n+1(1\times2)+(2\times2^2)+(3\times2^3)+\cdots+(n\times2^n)=2+(n-1)2^{n+1}(1×2)
+
(2×
22)+
(3×
23)+
⋯+
(n×
2n)=
2+
(n−
1)2n+1

for all integers n≥1n\geq1n≥1.

3 marks
Short answer