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, ..., 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.)

Answers for these exercises