Question

一道七年级数学题，急！！！

观察 ：
1^2+(1*2)^2+2^2=9=3^2 2^2+(2*3)^2+3^2=49=7^2
3^2+(3*4)^2+4^2=169=13^2
用含有n（n为正整数）的等式表示出来

Answer 1

n^2+(n(n+1))^2+(n+1)^2=(n(n+1)+1)^2,理由如下：
(n(n+1))^2+n^2+（n+1)^2
=(n(n+1)^2+(2n^2+2n+1)
=(n(n+1))^2+2(n(n+1))+1
=(n(n+1)+1)^2

Answer 2

这道题目真简单
答案是
n^2+[n*(n+1)]^2+(n+1)^2=(n^2+n+1)^2

Answer 3

用数学归纳法：
n^2＋[n(n＋1)]^2＋(n＋1)^2＝[n(n＋1)＋1]^2

Answer 4

n^2+[n*(n+1)]^2+(n+1)^2=[n*(n+1)+1]^2

Answer 5

n²+[n(n+1)]²+(n+1)²
=n²+(n²+n)²+(n+1)²
=n^4+2n^3+3n²+2n+1
=(n²+n)²+2(n²+n)+1
=(n²+n+1)²