n的平方加中括号里的n乘（n+1）的平方,加（n+1)的平方=中括号里的n乘(n+1)+1的平方.画化简以后的什么?

分类: 作业答案 • 2022-01-09 18:01:33

问题描述：

答

n^2+[n(n+1)]^2+(n+1)^2=[n(n+1)+1]^2
证：n^2+[n(n+1)]^2+(n+1)^2
=n^2+[n(n+1)]^2+n^2+2n+1
=[n(n+1)]^2+2n^2+2n+1
=[n(n+1)]^2+2n(n+1)+1
=[n(n+1)+1]^2