关于数学计算(按规律)1X2=3/1 X1X2X31X2+2X3=3/1 X2X3X41X2+2X3+3X4=3/1 X3X4X51X2+2X3+3X4+4X5=3/1 X4X5X6……(1)用带N的式子表示你发现的规律;(2)计算:1X2+2X3+3X4+……+100X(100+1).

问题描述:

关于数学计算(按规律)
1X2=3/1 X1X2X3
1X2+2X3=3/1 X2X3X4
1X2+2X3+3X4=3/1 X3X4X5
1X2+2X3+3X4+4X5=3/1 X4X5X6
……
(1)用带N的式子表示你发现的规律;
(2)计算:1X2+2X3+3X4+……+100X(100+1).

1X2+2X3+3X4+4X5+……+n*(n+1)=1*n*(n+1)*(n+2)/3
1X2+2X3+3X4+……+100X(100+1)=343400

1X2+2X3+3X4+……+n(n+1)=n(n+1)(n+2)/3
1X2+2X3+3X4+……+100X(100+1)
=100*101*102/3
=343400