1*2*3*4+1=25=5@:2*3*4*5+1=121=11@;3*4*5*6+1=361=19@.(n+1)(n+2)(n+3)(n+4)+1=?

问题描述:

1*2*3*4+1=25=5@:2*3*4*5+1=121=11@;3*4*5*6+1=361=19@.(n+1)(n+2)(n+3)(n+4)+1=?
@是平方

(n+1)(n+2)(n+3)(n+4)+1
=(n^2+5n+4)(n^2+5n+6)+1
=(n^2+5n+5-1)(n^2+5n+5+1)+1
=(n^2+5n+5)^2-1+1
=(n^2+5n+5)^2