Question

求证4个连续整数的积与1的和,必是完全平方公式

Answer 1

设为n-1,n,n+1,n+2

(n-1)*n*(n+1)*(n+2)+1

=(n^2+n)(n^2+n-2)+1

=(n^2+n)^2-2(n^2+n)+1

=(n^2+n-1)^2

得证