证明n^2+(n+3)^2+(n+5)^2+(n+6)^2=(n+1)^2+(n+2)^2+(n+4)^2+(n+7)^2整个等式对一切n都成立吗

证明n^2+(n+3)^2+(n+5)^2+(n+6)^2=(n+1)^2+(n+2)^2+(n+4)^2+(n+7)^2整个等式对一切n都成立吗
证明n^2+(n+3)^2+(n+5)^2+(n+6)^2=(n+1)^2+(n+2)^2+(n+4)^2+(n+7)^2整个等式对一切n都成立吗

证明n^2+(n+3)^2+(n+5)^2+(n+6)^2=(n+1)^2+(n+2)^2+(n+4)^2+(n+7)^2整个等式对一切n都成立吗
n^2+(n+3)^2+(n+5)^2+(n+6)^2=(n+1)^2+(n+2)^2+(n+4)^2+(n+7)^2
[(n+1)²-n²]+[(n+2)²-(n+3)²]+[(n+4)²-(n+5)²]+[(n+7)²-(n+6)²]=0
(2n+1)-(2n+5)-(2n+9)+(2n+13)=0
0=0
∴n^2+(n+3)^2+(n+5)^2+(n+6)^2=(n+1)^2+(n+2)^2+(n+4)^2+(n+7)^2整个等式对一切n都成立