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Chapter 8: Advanced Counting Techniques

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Discrete Mathematics and its Applications
Pages: 501 - 567
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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138 Questions for Chapter 8: Advanced Counting Techniques

  1. Find the coefficient of \({x^9}\) in the power series of each of these functions.

    Found on Page 549

  2. Find f(n)when n=2k, where fsatisfies the recurrence relation f(n)=f(n/2)+1with f(1)=1.

    Found on Page 535

  3. Solve the recurrence relationan=an-13an-22 if a0=2anda1=2 . (See the hint for Exercise 9.)

    Found on Page 567

  4. Give a big-\(O\) estimate for the function \(f\) in Exercise \(10\) if\(f\) is an increasing function.

    Found on Page 535

  5. Give a big- Oestimate for the functionf in Exercise 10 iff is an increasing function.

    Found on Page 535

  6. Find the coefficient of \({x^{10}}\) in the power series of each of these functions.

    Found on Page 549

  7. Find the solution of the recurrence relation an=3an-1-3an-2+an-3+1ifa0=2,a1=4anda2=8

    Found on Page 567

  8. Find the coefficient of \({x^{12}}\) in the power series of each of these functions.

    Found on Page 550

  9. 4. 12. Find \(f(n)\) when\(n = {3^k}\), where \(f\) satisfies the recurrence relation \(f(n) = 2f(n/3) + 4\) with\(f(1) = 1\).

    Found on Page 535

  10. Find the solution of the recurrence relation an=3an-1-3an-2+an-3if a0=2,a1=2, anda2=4.

    Found on Page 567

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