Try It Now

Work these exercises to see how well you understand this material.

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 $\binom{n}{k}$ .
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.
What is wrong with the following definition of f : ℝ → ℝ? f (0) = 1 and f(x) = f(x/2)/2 if x ≠ 0.