找规律并说明题观察下列各式:1*2*3*4+1=25=5⒉2*3*4*5+1=121=11⒉3*4*5*6+1=361=19⒉.从中你发现了什么规律?用数学语言叙述并说明.

n*(n+1)*(n+2)*(n+3)+1=(n^2+3n+1)

n*(n+1)*(n+2)*(n+3)+1=(n^2+3n+1)^2

规律:n(n+1)(n+2)(n+3)+1=(n^2+3n+1)^2
n(n+1)(n+2)(n+3)+1
=[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

N*(N+1)*(N+2)*(N+3)+1=(N+N+2+N+3+N+4+1)^2