1x2+2x3+3x4+.+999x1000

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1x2+2x3+3x4+.+999x1000
1x2+2x3+3x4+.+999x1000

1x2+2x3+3x4+.+999x1000
每一项这样拆：n*(n+1)=1/3[n*(n+1)(n+2)-(n-1)n(n+1)]
1x2+2x3+3x4+.+999x1000
=[(1x2x3-0x1x2)+(2x3x4-1x2x3)+(3x4x5-2x3x4)+.+(999x1000x1001-998x999x1000)]/3
=[999x1000x1001]/3
=333333000

1x2+2x3+3x4+。。。+999x1000
=1/3×999×1000×1001
=333333000

通项公式
n（n+1)(2n+1)/6+n(n+1)/2
＝999*(999+1)*(2*999+1)/6+999*(999+1)/2
＝333333000

1/1x2+1/2x3+1/3x4+1/4x5.1/9x10简算计算：1/1x2+1/2x3+1/3X4+...+1/9x10=? 1X2/1+2X3/1+3X4/1+……+9X10/1=_____ 计算：1/1x2+1/2x3+1/3X4+...+1/9x10=? -1/1x2-1/2x3-1/3x4-.-1/9x10 1x2/1+2x3/1+3x4/1+……+9x10/1 1/(1x2)+1/(2x3)+1/(3x4)+.+1/(9x10) 1X2/1—2X3/1—3X4/1—...—9X10/1=? 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11 1x2+2x3+3x4+.+999x1000 已知:x1=1/2+1/3,x2=1/3+1/4,x3=x2+x1,x4=x3+x2.,x10=x9+x8,求：x7/x1+x2+...+x10 1/1x2+1/2x3+1/3x4+……+1/9x1o= 1/1x2-1/2x3-1/3x4……-1/1x2+1/2x3+1/3x4+……+1/9x1o=1/1x2-1/2x3-1/3x4……-1/9x10= 用克拉默法则解下列方程组 x1-2x2+3x3-4x4=4 x2-x3+x4=-3 x1+3x2+2x4=1 -7x2+3x3+x4=3x1-2x2+3x3-4x4=4x2-x3+x4=-3 x1+3x2+2x4=1 -7x2+3x3+x4=3 解方程组X1-2x2+3x3-x4=1,3x1-x2+5x3-3x4=2,2x1+x2+2x3-2x4=3 写出方程组2*x1+x2-x3+x4=1,x1+2*x2+x3-x4=2,x1+x2+2*x3+x4=3的通解? 求非齐次线方程组的通解：2x1+x2-x3+x4=1 x1+2x2+x3-x4=2 x1+x2+2x3+x4=3 具体写出方程组：2x1+x2-x3+x4=1;x1+2x2+x3-x4=2;x1+x2+2x3+x4=3的通解练习一1．分解因式：(2)x10+x5-2；(4)(x5+x4+x3+x2+x+1)2-x5．2．分解因式：(1)x3+3x2-4；(2)x4-11x2y2+y2；(3)x3+9x2+26x+24；(4)x4-12x+323．3．分解因式：(1)(2x2-3x+1)2-22x2+33x-1；(2)x4+7x3+14x2+7x+1；(3)(x+y)3+2xy(1-x-y)-1；(