Mathematical Induction

Question 1

induction has two parts, a______________, where we show that P (1) is true, and an ________________, where we show that for all positive integers k, if P (k) is true, then P (k + 1) is true

Answer 1

basis step, inductive step

Question 2

The assumption that P (k) is true is called the

Answer 2

inductive hypothesis

Question 3

Use mathematical induction to prove this formula for the
sum of a nite number of terms of a geometric progression with initial term a and common ratio r

Answer 3

Sums of Geometric Progressions

Question 4

Use mathematical induction to show that if S is a
infinite set with n elements, where n is a nonnegative integer, then S has 2n subsets.

Answer 4

The Number of Subsets of a Finite Set