Question

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

2 is a factor of n2 - n + 2

Answer 1

Start by proving the base case: \(n=1\)

Answer 2

i dont know how too.

Answer 3

\[
(1)^2-(1)+2
\]

Answer 4

Show that it is a factor of \(2\)

Answer 5

of so'd it be (2)^2 - (2) + 2 ?

Answer 6

4 - 2 +2 = 4?

Answer 7

No, show that when \(n=1\) it's a factor of \(2\).

Answer 8

how do i that?

Answer 9

We are beyond high school now. We know how to substitute values into variables.

Answer 10

so it'd be 2 - 1 + 2? = 3

Answer 11

Okay so we have:\[
n^2 - n + 2
\]What does it equal when \(n=1\)?

Answer 12

1^2 - 1 + 2 = 2 - 1 +2 = 3?

Answer 13

\(1^2\neq 2\)

Answer 14

okay so the statement isnt true?

Answer 15

The problem is that you aren't doing the exponent correctly.\[
1^2=1\times 1=1
\]

Answer 16

Wait, are you trying to make fun of me?