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

You know how to use mathematical induction?
Show that it holds for n = 1 first, can you do that?

Answer 2

not really

Answer 3

Well that's a problem... first substitute 1 for n.

Answer 4

Simplify, and then see if that number is divisible by 2.

Answer 5

yes it is

Answer 6

i got an answer of two

Answer 7

Okay, good.
Now, the second step of mathematical induction is to ASSUME that it holds for n = k

Namely, we assume that
k^2 - k + 2 is divisible by 2,
catch me so far?

Answer 8

umm ok

Answer 9

how do we know its divisible

Answer 10

we know its divisible for k=1, which is important, we need to see if the (k+1) fits the same format

Answer 11

@BeastThatBeats
We don't *know* that it works for n = k, we ASSUME it.
Now, under that assumption, the most important step, substitute for n instead, k+1
And try to prove that it still yields an even number.

Answer 12

ok

Answer 13

i got k-k+4

Answer 14

is it right??

Answer 15

How did you get that?

Answer 16

K+1^2-k+1+2
k+1-k+1+2
k-k+1+1+2
k-k+4

Answer 17

lol no
\[\Large (k+1)^2 = \color{red}?\]

Answer 18

whats the answer

Answer 19

k^2 +k+2

Answer 20

Nope... at this level, multiplying polynomials should be second nature, tsk XD
\[\Large (k+1)^2 = k^2 + \color{red}{2}k + \color{red}1 \]

Answer 21

then

Answer 22

umm are you there...