Question

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

P(n)=n^2-n+2
P(1)=1^2-1+2=0,which is a multiple of 2
P(1) is true.
Assume that P(k) is true.
P(k)=k2-k+2=2t (say)
k^2=2t+k-2
P(k+1)=(k+1)^2-(k+1)+2
=k^2+2k+1-k-1+2
=K^2+k+2
=2t+k-2+k+2
=2t+2k
=2(t+k)
=2*an integer
Hence P(k+1) is true.
By induction P(n) is true for all n (positive integer).

Answer 2

Thank you yeah i just figured some of this out i have another one i need help on