1X2+2X3+3X4+4X5...+2011X2013=

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1X2+2X3+3X4+4X5...+2011X2013=1X2+2X3+3X4+4X5...+2011X2013=1X2+2X3+3X4+4X5...+2011X2013=n(n+1)=n²

1X2+2X3+3X4+4X5...+2011X2013=
1X2+2X3+3X4+4X5...+2011X2013=

1X2+2X3+3X4+4X5...+2011X2013=
n(n+1)=n²+n
1*2=1²+1
2*3=2²+2
3*4=3²+3
-----
n(n+1)=n²+n
1X2+2X3+3X4+4X5...+n(n+1)
=(1²+2²+3²+----+n²)+(1+2+3+---+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=(1/6)n(n+1)(2n+1+3)=n(n+1)(n+2)/3
把n=2012代入得:
1X2+2X3+3X4+4X5...+2012X2013
=2012*2013*2014/3=2012*671*2014=2719004728

1X2+2X3+3X4+4X5...+2012X2013
=1/3X1X2X3+1/3[2X3X4-1X2X3]+1/3[3X4X5-2X3X4]+....+1/3[2012X2013X2014-2011X2012X2013]
=1/3X2012X2013X2014
=2719004728

1X2+2X3+3X4+4X5...+2011X2013=
=1/3 (1×2×(3-0)+2×3×(4-1)+3×4×(5-2)+.....+2011×2012×(2013-2010))
=1/3× (1×2×3-0×1×2+2×3×4-1×2×3+3×4×5-2×3×4+......+2011×2012×2013-2010×2011×2012)
=1/3 × (2011×2012×2013)
=2714954572

裂项消元法 结果-2012
原式=1/(1/1-1/2) 1/(1/2-1/3) 1/(1/3-1/4) 1/(1/4......-1/2012 1/(1/2012-1/2013)=1-1/1/2013=-2012

1x2+2x3+3x4+4x5+.+15x16 x1-x2+x3=1 x2-x3+x4=2 x3-x4+x5=3 x4-x5+x1=4 x5-x1+x2=5 求x1,x2,x3,x4,x5 求非齐次线性方程组的通解x1+3x2+5x3-4x4=1x1+3x2+2x3-2x4+x5=-1x1-2x2+x3-x4-x5=3x1+2x2+x3-x4-x5=3 解一道方程组x1+x2+x3=5,x2+x3+x4=1,x3+x4+x5=-5,x4+x5+x1=-3,x5+x1+x2=2 若x1,x2,x3,x4,x5满足方程组:x1-x2+x3=1 x2-x3+x4=2 x3-x4+x5=3 x4-x5+x1=4 x5-x1+x2=5 求x2,x3,x4的少打了个字,是求x2,x3,x4的值 x1-x2+x3=1x2-x3+x4=21若x1,x2,x3,x4,x5满足方程组 x3-x4+x5=3x4-x5+x1=4x5-x1+x2=5求x2 x3 x4的值2已知 x1+x4+x6+x7=39 x2+x4+x5+x7=49 x3+x5+x6+x7=41 x4+x7=13 x5+x7=14 x6+x7=9 x1+x2+x3+x4+x5+x6+x7=9求x7的值若x1,x2,x3,x4,x5满足方程组 x1-x 解方程组:x1+x2+x3+x4+x5=7 3x1+2x2+x3+x4-3x5=-2 x2+2x3+2x4+6x5=23 5x1+4x2-3x3+3x4-x5=10 求非其次线性方程组 {x1+2x2+x3+x4+x5=1x1+2x2+x3+x4+x5=12x1+4x2+3x3+x4+x5=2-x1-2x2+x3+3x4-x5=5 2x3+4x4-2x5=6 的一般解 求线性方程组的全部解,并用对应导出组的基础解系表示X1+3X2+5X3-4X4=1 X1+3X2+2X3-2X4+X5=-1 X1-2X2+X3-X4-X5=3 X1-4X2+X3+X4-X5=3 X1+2X2+X3-X4+X5=-1 简算:1/1x2+1/2x3+1/3x4+1/4x5 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 求解线性方程组 x1-2x2+3x3-x4-x5=2 x1+x2-x3+x4-2x5=1 2x1-求解线性方程组x1-2x2+3x3-x4-x5=2x1+x2-x3+x4-2x5=12x1-x2+x3-2x5=22x1+2x2-5x3+2x4-x5=5 已知数据x1,x2,x3,x4,x5的平均数是20,那么另一组数据x1,x2+1,x3+2,X4+3,X5+4的平均数 求下列非齐次线性方程组的通解(1){x1+x2+x3+x4+x5=2;x1+2x2-4x5=-2;x1+2x3+2x4+6x5=6;4x1+5x2+3x3+3x4-x5=4}(2){x1-x2+5x3-x4=1;x1+x2-2x3+3x4=1;2x1+3x3+2x4=2;2x1+4x2-11x3+10x4=2}(3){x1+x2+x3+x4+x5=1;3x1+2x2+x3+x4-3x5=0 简算.1/1X2+1/2X3+1/3X4+1/4X5+.+1/199X200, 1x2/1+2x3/1+3x4/1+4x5/1+…+39x40/1 求1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+.+1/(2005x2006) 1/1x2+1/2x3+1/3x4+1/4x5.1/9x10简算 1/1x2+1/2x3+1/3x4+1/4x5+.1/49x50