To prove: If n is positive integer, then
Explanation of Solution
Proof:
Use mathematical induction on n.
Let
Base case:
To prove that the statement is true for
Clearly, it is divisible by 6.
Therefore, the statement is true for
Induction hypothesis:
Assume that the claim is true for
That is,
Thus
Inductive step:
To prove that the statement is true for
Thus, the statement is true for
Therefore, by mathematical induction, the statement
Hence the required result is obtained.
Chapter 1 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition