n{n+1}{n+2}{n+3}+1是哪个数的平方,并说明理由
问题描述：
n{n+1}{n+2}{n+3}+1是哪个数的平方,并说明理由
答
n(n^2+3n+2)(n+3)+1
=n(n^3+6n^2+11n+6)+1
=n^4+6n^3+11n^2+6n+1
=(n^4+6n^3+9n^2)+(2n^2+6n)+1
=(n^2+3n)^2+2(n^2+3n)+1
=(n^2+3n+1)^2
答
=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