题目

找规律1²+（1×2）²+2²=9=3²
2²+﹙2×3﹚²+3²=49=7²
3²+﹙3×4﹚²+4²=169=13²
求助啊~~急!（⊙ω⊙）~~

提问时间：2020-07-30

答案

n^2 + [n*(n+1)]^2 + (n+1)^2 = [n*(n+1)+1]^2
很明显等式成立.
因为右式[n*(n+1)+1]^2展开为
[n*(n+1)+1]^2 = [n*(n+1)]^2 +2n(n+1) +1
= [n*(n+1)]^2 +2n^2+2n +1
= [n*(n+1)]^2 +(n^2+2n +1)+n^2
= [n*(n+1)]^2 +(n+1)^2+n^2
= 左式