1/1x2+1/2x3+1/3x4+.+1/n(n+1)=?1/2x4+1/4x6+1/6x8+…+1/2010x2012

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/04 10:47:27
1/1x2+1/2x3+1/3x4+.+1/n(n+1)=?1/2x4+1/4x6+1/6x8+…+1/2010x2012

1/1x2+1/2x3+1/3x4+.+1/n(n+1)=?1/2x4+1/4x6+1/6x8+…+1/2010x2012
1/1x2+1/2x3+1/3x4+.+1/n(n+1)=?
1/2x4+1/4x6+1/6x8+…+1/2010x2012

1/1x2+1/2x3+1/3x4+.+1/n(n+1)=?1/2x4+1/4x6+1/6x8+…+1/2010x2012
1/1x2+1/2x3+1/3x4+.+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+···+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)

1/1x2+1/2x3+1/3x4+......+1/n(n+1)=1-1/2+1/2-1/3+1/3-1/4......+1/n-1/(n+1)=1-1/(n+1)=n/(n+1)

1/n(n+1)=1/n-1/(n+1)
所以1/1x2+1/2x3+1/3x4+......+1/n(n+1)=1-1/2+1/2-1/3+……+1/n-1/(n+1)=1-1/n
1/2x4+1/4x6+1/6x8+…+1/2010x2012 =1/2(1/2-1/4+1/4-1/6+……+1/2010-1/2012)=1/2×(1/2-1/2012)=1005/4024

原式=1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)=1-1/(n+1)

原式=1-1/2+(1/2-1/3)+（1/3-1/4）+。。。。+（1/n-1/(n+1)）=1-1/2+1/2-1/3+......+1/n-1/(n+1)=1-1/(n+1)=n/(n+1)

由公式 1/nx（n+m）=m（1/n-1/n+m）
所以1、1/1-1/2+1/2-1/3+1/3-1/4.......................1/n-1/n+1=1-1/n+1=n/n+1 （中间的每2项可以消去）
2、2（1/2-1/4+1/4-1/6......................1/2010-1/2012）=2*(1/2-1/2012)=1-1/1006=1005/1006

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 因式分解：x4+x3+2x2 +x+1 解方程组X1-2x2+3x3-x4=1,3x1-x2+5x3-3x4=2,2x1+x2+2x3-2x4=3 x1+5x2-x3-x4=-1x1-2x2+x3+3x4=33x1+8x2-x3+x4=1 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 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 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+.+2011x2012 1x2+2x3+3x4+4x5+.+15x16 1x2+2x3+3x4+.+100x101= 1x2+2x3+3x4+.+100x101=?结果 1x1!+2x2!+3x3!+4x4!.nxn! 1X2+2x3+3x4+……+2013x2014 1x2+2x3+3x4+.+19x20