怎样证明n[n+2]+1=[n+1]的平方

网友回答

左边=n(n+2)+1=n^2+2n+1
右边=(n+1)^2=n^2+2n+1
所以左边=右边……
======以下答案可供参考======
供参考答案1:
n[n+2]+1=n^2+2n+1=(n+1)^2得证
供参考答案2:
A= n(n+2)+1= n²+2n+1
B= (n+1)²=(n+1) ×(n+1)
=(n+1) ×n+(n+1)
= n²+2n+1
∵A-B=( n²+2n+1)-( n²+2n+1)=0
∴A=B 即n(n+2)+1=(n+1)²