If n is a natural number, then n(n+1)(n+2)(n+3)+1 is always:
Show answer & explanation
Correct answer: A
Explanation
Given:
n(n+1)(n+2)(n+3) + 1
Let a = n² + 3n
n(n+1)(n+2)(n+3)
= n(n+3)(n+1)(n+2)
= a(a + 2)
a(a + 2) + 1 = a² + 2a + 1
= (a + 1)²
= (n² + 3n + 1)²
Thus, it is always a perfect square.