**Unit 17 Exercises**

**1. **Find a formula for

1/2 + 1/4 + 1/8 + ... + 1/2^{n}

^{ }by examining the values of this expression
for small values of *n*. Use mathematical induction to prove your result.

**2.** Show that if *a*_{1},
*a*_{2}, ..., *a*_{n} are *n* distinct real numbers,
exactly *n - 1* multiplications are used to compute the product of these
*n* numbers no matter how parentheses are inserted into their product.
(*Hint*: Use the second principle of mathematical induction and consider the last
multiplication.)