Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.4 Mathematical Induction - 11.4 Assess Your Understanding - Page 850: 21

See below.

1. Test for $n=1$, we have $1^2-1+2=2$ is divisible by 2, thus it is true. 2. Assume the statement is true for $n=k$, we have $k^2-k+2=2$ is divisible by 2 3. For $n=k+1$, we have $(k+1)^2-(k+1)+2=k^2+2k+1-k-1+2=(k^2-k+2)+2k$ which contains two part and both are divisible by 2, thus it is true for $n=k+1$ 4. We conclude that the statement is true for any $n$.