n(n+1)(n+2)(n+3)+1=[(n+1)(n+2)-1]^2
证明:
n(n+1)(n+2)(n+3)+1
=(n+1)(n+2)(n^2+3n)+1
=(n+1)(n+2)(n^2+3n+2-2)+1
=(n+1)(n+2)[(n+1)(n+2)-2]+1
=[(n+1)(n+2) ]^2-2(n+1)(n+2)+1
=[(n+1)(n+2)-1]^2
推论为:n*(n+1)*(n+2)*(n+3)+1=[n*(n+3)+1]的二次方!由于用手机稍微有点麻烦,就有劳楼主验证了!希望楼主满意
n(n+1)(n+2)(n+3)=(2n平方+3)的二次方