Question

1^2+4^2+6^2+7^2=2^2+3^2+5^2+8^2 找规律.

Answer 1

规律：

n^2+(n+3)^2+(n+5)^2+(n+6)^2=(n+1)^2+(n+2)^2+(n+4)^2+(n+7)^2

证明：

左边=n^2+n^2+6n+9+n^2+10n+25+n^2+12n+36=4n^2+28n+70

右边=n^2+2n+1+n^2+4n+4+n^2+8n+16+n^2+14n+49=4n^2+28n+70

所以,

n^2+(n+3)^2+(n+5)^2+(n+6)^2=(n+1)^2+(n+2)^2+(n+4)^2+(n+7)^2