1/2x4+1/3x5+1/4x6+1/5x7+.1/8x10+1/9x11

来源：学生作业帮助网编辑：作业帮时间：2024/05/13 03:12:22

1/2x4+1/3x5+1/4x6+1/5x7+.1/8x10+1/9x11
1/2x4+1/3x5+1/4x6+1/5x7+.1/8x10+1/9x11

1/2x4+1/3x5+1/4x6+1/5x7+.1/8x10+1/9x11
1/2x4+1/3x5+1/4x6+1/5x7+.1/8x10+1/9x11
=(1/2x4+1/4x6+1/6x8+1/8x10)+(13x5+1/5x7+1/7x9+1/9x11)
=(1/2)[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+(1/8-1/10)]+(1/2[(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]
=(1/2)(1/2-1/10)+(1/2)(1/3-1/11)
=1/5+4/33
=53/165

先列一个通式吧
1/[n(n+2)]=0.5*[1/n -1/(n+2)]
所以原式可以化成
0.5*(1/2-1/4+1/3-1/5+1/4-1/6.........+1/9-1/11)=
0.5*[(1/2+1/3+1/4+1/5+...+1/9)-(1/4+1/5...+1/11)=
0.5*(1/2+1/3-1/10-1/11)=0.5*106/165=53/165
所以原式=53/165

1/1x3+1/2x4+1/3x5+1/4x6+...+1/100x102=? 1/1x3+1/2x4+1/3x5+1/4x6+...+1/10x12 1x3+2x4+3x5+4x6..+99x101=? 1x2+2x3+3x4+4x5+5x6---+99x100=? 1x2+2x3+3x4+4x5+5x6+.+99x100 巧算：1x2+2x3+3x4+4x5+5x6+6x7...+8x9 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 1/1x3+1/2x4+1/3x5+1/4x6+1/5x7+1/6x8 1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+......1/2008x2009 1/1x2+2/1x3+3/1x4+4/1x5+5/1x6+6/1x7= 1/2x4+1/3x5+1/4x6+1/5x7+.1/8x10+1/9x11 1/2x4+1/3x5+1/4x6+1/5x7+...+1/97x99=?RT 1x3＋2x4＋3x5＋4x6……＋100x102＝? 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11 (2X2)/1X3+(4X4)/(3X5)+(6X6)/(5X7)+...+(20X20)/(19X21)==? 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9= 1x1-2x2+3x3-4x4+5x5-6x6.-100x100+101x101简便算法答案 2013/1x2+2013/2X3+2013/3X4+2013/4X5+2013/5X6简便计算,