Question

help please

Answer 1

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 2

If we want to show if it is a factor of 2, our target is to make the final result be 2 times sth
For M.I., there are several steps
1) Prove if it is true for n=1.
directly substitute n=1 into n^2 -n +2, you can get the number which is divisible by 2. (I believe you can do it yourself)

2) Assume it is true for n=k.
That means that k^2 -k+2=2M (where M is a integer)

3) Prove it is true for n=k+1
Substitute n=k+1 into n^2 -n+2
(k+1)^2 -(k+1)+2= ....... <--expand it my yourself.
After expansion, you will probably find some terms which is exactly the same as the assumption we make. Group those terms and write them as 2M. Then, for the remaining terms, you will probably make them to be 2 time sth.

Then we can show it is true.

Share your steps below. Then I can give some comments for you.