解;规律; n(n+1)(n+2)(n+3)+1=(n*(n+3)+1)^2
说明: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)^2+1)^2
解;规律; n(n+1)(n+2)(n+3)+1=(n*(n+3)+1)^2
说明: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)^2+1)^2