Question

PLZZZZZ HELPP!!!!

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

2 is a factor of n^2 - n + 2

Answer 1

\[ \large 2\mid(n^2-n+2) \]

Answer 2

if n=1 then
\[ \large n^2-n+2=1^2-1+2=2 \]
which is a multiple of 2.

Answer 3

let's assume that n>1 and
\[ \large 2\mid(n^2-n+2) \]
we have to prove that
\[ \large 2\mid[(n+1)^2-(n+1)+2] \].

Answer 4

Let's see
\[ \large (n+1)^2-(n+1)+2=n^2+2n+1-n-1+2 \]
\[ \large =(n^2-n+2)+2n=2\cdot\alpha+2n=2(\alpha+n) \]

Answer 5

ok.

Answer 6

where did the a come from?

Answer 7

don't forget that
\[ \large 2\mid(n^2-n+2)\quad\Leftrightarrow\quad n^2-n+2=2\cdot\alpha \]
this the induction hipothesis.

Answer 8

oh yes i forgot.

Answer 9

so that is it??

Answer 10

yes!!!
do u know how to do induction??

Answer 11

kind of. but you really helped!! thank u soo much!!

Answer 12

u r welcome
glad to help