Question

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 2 is a factor of n2 + 7n

Answer 1

Let S(n) the statement, 2 is a factor of $n^2 +7n$.

For n=1, 1^2 + 7(1) = 1 + 7 = 8, 1 is a factor of 8, then S(1) is true.

For n=2, we have 2^2 +7(2) = 4 +14 = 18, of course, 2 is a factor of 18, then S(2) is true.

For n=3, we have 3^2 +7(3) = 9 +21 = 30, of course, 2 is a factor of 30, then S(3) is true.