1*2*3*4+1=25=5² 2*3*4*5+1=121=11² (n+1)(n+2)(n+3)(n+4)+1=?²

问题描述:

1*2*3*4+1=25=5² 2*3*4*5+1=121=11² (n+1)(n+2)(n+3)(n+4)+1=?²

(n+1)(n+2)(n+3)(n+4)+1
=[(n+1)(n+4)][(n+2)(n+3)]+1
=(n²+5n+4)(n+5n+6)+1
=(n²+5n+5)²