**Unit 16 Exercises**

**1. **Use mathematical induction to prove that 3 + 3 * 5 +
3 * 5^{2}+ ... + 3 * 5^{n} =
3 (5^{n+1} - 1)/4 whenever *n* is a nonnegative integer.

**2.** Prove that 1^{2} + 3^{2} +
5^{2}+ ... + (2*n* + 1)^{2} =
(*n* + 1)(2*n* + 1)(2*n*+ 3)/3 whenever *n* is a nonnegative integer.

**3.** Show that 2^{n} >
*n*^{2}whenever *n* is an integer greater than 4.

**4.** Show that any postage that is a positive integer number of cents
greater than 7 cents can be formed using just 3-cent stamps and 5-cent stamps.

**5.** Use mathematical induction to show that 5 divides
*n*^{5}- *n* whenever *n* is a nonnegative integer.

**6.** Use mathematical induction to prove that if *A*_{1},
*A*_{2}, ...*A*_{n} are subsets of a universal set *U*,
then

*Ai = *