Use mathematical induction to prove that the statement is true for every positive integer n.2 is a factor of

Question

What will be an ideal response?

Answer 1

Show S₁ is true: 1² - 1 + 2 = 2; 2 is a factor of 2
Assume that S_k is true: ; 2 is a factor of k² - k + 2
Show that if S_k is true, then S_k+1 is true:
 S_k+1 = (k + 1)² - (k + 1) + 2 = k² + k + 2 = (k² - k + 2) + 2k
 (k² - k + 2) is S_k and 2 is a factor of 2k
Since 2 is a factor of S_k+1 is true, the statement is true for all values of n.