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H2 Math Summary Notes

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  1. Pure Mathematics

    Unit 1 Inequalities
    1 Question
  2. Unit 2 Graphing Techniques
    7 Questions
  3. Unit 3 Transformation of Graphs
    2 Questions
  4. Unit 4 Functions
    6 Questions
  5. Unit 5 APGP & Recurrence Relations
    6 Questions
  6. Unit 6 Sigma Notation
    6 Questions
  7. Unit 7 Techniques of Differentiation
    2 Questions
  8. Unit 8 Applications of Differentiation
    9 Questions
  9. Unit 9 Maclaurin Series
    2 Questions
  10. Unit 10 Techniques of Integration
    6 Questions
  11. Unit 11 Applications of Integration
    4 Questions
  12. Unit 12 Differential Equations
    2 Questions
  13. Unit 13 Vectors
    11 Questions
  14. Unit 14 Complex Numbers
    6 Questions
  15. Statistics
    Unit 15 Permutation and Combinations
    7 Questions
  16. Unit 16 Probability
    5 Questions
  17. Unit 17 Discrete Random Variable
    4 Questions
  18. Unit 18 Binomial Distribution
    5 Questions
  19. Unit 19 Normal Distribution
    7 Questions
  20. Unit 20 Sampling and Estimation
    8 Questions
  21. Unit 21 Hypothesis Testing
    6 Questions
  22. Unit 22 Correlation and Linear Regression
    5 Questions
Lesson Progress
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A sequence of negative numbers is defined by \({{x}_{n+1}}=-\sqrt{8+3{{x}_{n}}}\) for \(n=1\), \(2\), \(3\), …

(i)

Show that \(-\frac{8}{3}<{{x}_{n}}<0\) for \(n=1\), \(2\), \(3\), …

(ii)

Find the exact value of \(l\), given that when \(n\to \infty \), \({{x}_{n}}\to l\).

(iii)

Show that \({{x}_{n+1}}^{2}-{{l}^{2}}=3\left( {{x}_{n}}-l \right)\).

(iv)

Show algebraically that if \({{x}_{n}}<l\) for some value of \(n\), then \({{x}_{n+1}}>l\).

Responses