1X2=1⼀3(1X2X3-0X1X2) 2X3=1⼀3(2X3X4-1X2X3) 发现1X2+2X3+3X4+、、、、、、+nX(n+1)=?

写原因,理由
2024-12-17 05:39:23
推荐回答(1个)
回答1:

根据以上规律:
3X4=1/3(3X4X5-2X3X4)
nX(n+1)=1/3[nX(n+1)X(n+2)-(n-1)XnX(n+1)]
1X2+2X3+3X4+、、、、、、+nX(n+1)=1/3[1X2X3-0X1X2+2X3X4-1X2X3+3X4X5-2X3X4+...+nX(n+1)X(n+2)-(n-1)XnX(n+1)]=1/3[nX(n+1)X(n+2)-0X1X2]=n(n+1)(n+2)/3