Let P(n):n2+n+1 is an even integer. If p(k) is assumed true ⇒P(k+1)  is true. Therefore, P(n) is TRUE

Given,P(n):n2+n+1At n = 1, P(1):3, which is not an even integer. P(1 ) is not true (principle of induction is not applicable). Also, n(n + 1 ) + 1 is always an odd integer.