阅读下列材料:1X2=1/3(1X2X3-0X1X2),
2X3=1/3(2X3X4-1X2X3),
3X4=1/3(3X4X5-2X3X4),
有以上三个等试相加,可得
1X2+2X3+3X4=1/3X3X4X5=20
请计算下题:
(1)、1X2+2X3+3X4+···+10X11(写过程)
(2)、1X2+2X3+3X4+···+nX(n+1)=?
(3)、1X2X3+2X3X4+3X4X5+···7X8X9=?
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追çåçï¼2ï¼1X2+2X3+3X4+···+nX(n+1)=1/3[n+(n+1)+(n+2)]
(3)1X2X3=1/4(1X2X3X4-0X1X2X3)
2X3X4=1/4(2X3X4X5-1X2X3X4)
3X4X5=1/4(3X4X5X6-2X3X4X5)
4X5X6=1/4(4X5X6X7-3X4X5X6)
5X6X7=1/4(5X6X7X8-4X5X6X7)
6X7X8=1/4(6X7X8X9-5X6X7X8)
7X8X9=1/4(7X8X9X10-6X7X8X9)
ä¸å¼ç¸å å¾ï¼
1X2X3+2X3X4+3X4X5+···7X8X9=1/4(7X8X9X10ï¼ï¼1260