证明：
n(n+1)(n+2)(n+3)+1
=n(n+3)(n+1)(n+2)+1
=(n^2+3n)(n^2+3n+2)+1
令n^2+3n＝X
上式=X(X+2)+1
=X^2+2X+1
=(X+1)^2
该式为完全平方式