Question

观察等式:1*2*3*4+1=5^2=(1^2+3*1+1)^2

Answer 1

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

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

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

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