Question

help plz

Answer 1

@surjithayer

Answer 2

2 is a factor of n^2-n+2
means n^2-n+2 is divisible by 2
Let P(n)=n^2-n+2
P(1)=1^2-1+2=2 which is divisible by 2
Hence P(1) is true.
Assume that P(k) is true
or k^2-k+2 is divisible by 2
Let k^2-k+2=2 m, where m is an integer.
k^2=2m+k-2
P(k+1)=(k+1)^2-(k+1)+2=k^2+2k+1-k-1+2
=2 m+k-2+2k+1-k-1+2
=2m+2k+2
=2(m+k+1)
=2* an integer.
or P(k+1) is divisible by 2
Hence by induction P(n) is true for all n