n n\,n is an integer. Prove algebraically that the sum of n(n+1)n(n + 1)n(n+1) and n+1n + 1n+1 is always a square number. You may use n2+2n+1=(n+1)2n^2 + 2n + 1 = (n + 1)^2n2+2n+1=(n+1)2.
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