1x2+2x3+3x4+.+2011x2012

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1x2+2x3+3x4+.+2011x2012
1x2+2x3+3x4+.+2011x2012

 

1x2+2x3+3x4+.+2011x2012
整数裂项
1/(2011×2012)×(1×2+2×3+...+2011×2012)
=1/(2011×2012)×(2011×2012×2013)/3
=2013/3
=671

1x2+2x3+3x4+。。。+2011x2012
= 2011x2012x2013 / 3

所以 最后算式 = 2013/3 = 671

2011*2012*2013/3

由题意
1x2+2x3+3x4+。。。+2011x2012
=2010x(2011x2012) / 3+3x(2011x2012)/3
=2011x2012x2013/3

所以上面结果就是
(1/2011x2012) x 2011x2012x2013/3
=2013/3

=671

671

=1/(2011*2012)*2011*2012*2013/3
=2013/3=671

因为1x2+2x3+3x4+。。。+2011x2012 共有2011项,
所以
1x2+2x3+3x4+。。。+2011x2012=2011X2012X2013/3
[1/(2011X2012)]X1x2+2x3+3x4+。。。+2011x2012
=[1/(2011X2012)]X2011X2012X2013/3
=2013/3=671

根据上面列出的规律，可以得出：

（1x2+2x3+3x4+…+2011x2012）=(2011x2012x2013)/3

所以：

1/（2011x2012）x（1x2+2x3+3x4+…+2011x2012)=2013/3 

 

 

 

 

 

(1*2+2*3+3*4.....+2011*2012)/(2011*2012)

=2011*2012*2013/3/(2011*2012)=2013/3=671

1x2+2x3+3x4+.+2011x2012 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 x1+5x2-x3-x4=-1x1-2x2+x3+3x4=33x1+8x2-x3+x4=1 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 因式分解x4+x3+2x2-x+3 因式分解：x4+x3+2x2 +x+1 用初等行变换来解下列线性方程组（1）2x1-x2+3x3=3 3x1+x2-5x3=0 4x1-x2+x3=3 x1+3x2-13x3=-6(2) x1-2x2+x3+x4=1 x1-2x2+x3-x4=-1 x1-2x2+x3-5x4=5(3) x1-x2+x3-x4=1 x1-x2-x3+x4=0 x1-x2-2x3+2x4=-1/2 1X2+2X3+3X4+.NX(N+1) 1X2+2X3+3X4+.NX(N+1)规律 1x2+2x3+3x4+4x5+.+15x16 1x2+2x3+3x4+.+100x101= 1x2+2x3+3x4+.+100x101=?结果 1x1!+2x2!+3x3!+4x4!.nxn! 1X2+2x3+3x4+……+2013x2014