Exercises

  1. By the recursive definition of binomial coefficients, \binom{7}{2} = \binom{6}{2} + \binom{6}{1}. Continue expanding \binom{7}{2} to express it in terms of quantities defined by the basis. Check your result by applying the factorial definition of \binom{n}{k}.

  2. Let p(x) = x5 + 3x4− 15x3 + x − 10.
    1. Write p(x) in telescoping form.
    2. Use a calculator to compute p(3) using the original form of p(x).
    3. Use a calculator to compute p(3) using the telescoping form of p(x).
    4. Compare your speed in parts b and c.

  3. What is wrong with the following definition of f : ℝ → ℝ? f (0) = 1 and f(x) = f(x/2)/2 if x ≠ 0.

 

Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/ads-latex/ads.pdf
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