n(n+1)(n+2)(n+3)+1=(n^2+3n+1)^2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=(n^2+3n)^2+2*(n^2+3n)+1=(n^2+3n+1)^2