Unit 17 Exercises
1. Find a formula for
1/2 + 1/4 + 1/8 + ... + 1/2n
by examining the values of this expression for small values of n. Use mathematical induction to prove your result.
2. Show that if a1, a2, ..., an 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.)
Answers for these exercises