1×2×3×4+1=25=5的2次方 2×3×4×5+1=121=11的平方

2024-12-18 16:32:00
推荐回答(3个)
回答1:

n(n+1)(n+2)(n+3)+1=[(n+1)(n+2)-1]^2
证明:
n(n+1)(n+2)(n+3)+1
=(n+1)(n+2)(n^2+3n)+1
=(n+1)(n+2)(n^2+3n+2-2)+1
=(n+1)(n+2)[(n+1)(n+2)-2]+1
=[(n+1)(n+2) ]^2-2(n+1)(n+2)+1
=[(n+1)(n+2)-1]^2

回答2:

推论为:n*(n+1)*(n+2)*(n+3)+1=[n*(n+3)+1]的二次方!由于用手机稍微有点麻烦,就有劳楼主验证了!希望楼主满意

回答3:

n(n+1)(n+2)(n+3)=(2n平方+3)的二次方