這個問題,我相當熟悉了,分析出來,你認真看吧.
1X2 +2X3 +3X4
= (1X2X3 +2X3X3 +3X4X3) /3
= [ 1X2X3 +2X3X(4-1) +3X4X(5-2) ] /3
= [ 1X2X3 -1X2X3 +2X3X4 -2X3X4 +3X4X5 ] /3
= 3X4X5 /3
1X2 +2X3 +3X4 +4X5
= (1X2X3 +2X3X3 +3X4X3 +4X5X3) /3
= [ 1X2X3 +2X3X(4-1) +3X4X(5-2) +4X5X(6-3) ] /3
= [ 1X2X3 -1X2X3 +2X3X4 -2X3X4 +3X4X5 -3X4X5 +4X5X6 ] /3
= 4X5X6 /3
規(guī)律你看出來了嗎?這個數(shù)列的公式就是
通項 a= n(n+1)
前n項數(shù)列和 S= n(n+1)(n+2)/3
這樣一來,一直加到 99X100,就是
1X2 +2X3 +3X4 +4X5 +……+99X100
= 99X100X101 /3
= 333300