计算:n(n+1)(n+2)(n+3)+1.

问题描述:

计算:

n(n+1)(n+2)(n+3)+1

原式=

[n(n+3)[(n+1)(n+2)]+1

=
(n2+3n)[(n2+3n)+2]+1

(n2+3n)2+2(n2+3n)+1

=
(n2+3n+1)2

=n2+3n+1.