Question

找规律1²+（1×2）²+2²=9=3²

Answer 1

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