Chapter 9.5, Problem 37E

Solution

To identify : If the goal of mathematical induction is to prove that a statement $P_n$ is true for all real numbers $n$ .

False

Given information :

The statement $P_n$ .

Explanation :

The method of mathematical induction is defined as a method that proves a statement to be true for every natural number. This means it will prove any statement to be true for positive integers only.

The method starts with proving the statement $P_n$ to be true for $n=1$ .

Then, it is assumed that the statement $P_n$ is true for $n=k$ and it is proved true for $n=k+1$ also.

Thus, the statement “the goal of mathematical induction is to prove that a statement $P_n$ is true for all real numbers $n$ ” is false.