For all natural value of n, the number n2+n+3 is

For all natural value of n, the number n2+n+3 is Correct Answer always odd

n2 + n + 3  =  n(n + 1) + 3 If n is even, n + 1 is odd " n " odd, n + 1 is even The product n(n + 1) is always even since one of the term is always even. So, n2 + n + 3  is always odd.
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