1/1X2 +1/2X3+1/3X4+……1/10X11

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1/1X2 +1/2X3+1/3X4+……1/10X11

1/1X2 +1/2X3+1/3X4+……1/10X11
1/1X2 +1/2X3+1/3X4+……1/10X11

1/1X2 +1/2X3+1/3X4+……1/10X11
1/1X2 +1/2X3+1/3X4+……1/10X11
=(1/1-1/2)+(1/2-1/3)+……+(1/10-1/11)
=1/1-1/11
=10/11

1/n×(n+1)=1/n-1/(n+1)
1/1×2+1/2×3+...+1/10×11
=(1/1-1/2)+(1/2-1/3)+...+(1/10-1/11)
=1-1/11
=10/11

=(1-1/2)+(1/2-1/3)+......(1/10-1/11)=1-1/11=10/11

解:利用公式1/n*(n+1)=(1/n)-(1/n+1).
原式=1-1/2+1/2-1/3......+1/10-1/11
=1-1/11
=10/11

如果想证明公式,倒过来算算就行了.

1X2+2x3+3x4+……+2013x2014 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+.+19x20