经典奥数题11/1x3+1/3x5+1/5x7.1/99x101解题思路请写清楚

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/16 13:26:28
经典奥数题11/1x3+1/3x5+1/5x7.1/99x101解题思路请写清楚

经典奥数题11/1x3+1/3x5+1/5x7.1/99x101解题思路请写清楚
经典奥数题1
1/1x3+1/3x5+1/5x7.1/99x101
解题思路请写清楚

经典奥数题11/1x3+1/3x5+1/5x7.1/99x101解题思路请写清楚
1/a-1/(a+2)=2/[a*(a+2)]
所以
1/[a*(a+2)]=1/2*[1/a-1/(a+2)]
1/1x3=1/2(1-1/3)
1/3x5=1/2(1/3-1/5)
1/5x75=1/2(1/5-1/7)
.
1/99x101=1/2(1/99-1/101)
于是:
1/1x3+1/3x5+1/5x7.1/99x101
=1/2*(1-1/3+1/3-1/5+1/5-1/7+.+1/99-1/101)
=1/2(1-1/101)
=50/101

=1-1/3+1/3-1/5....-1/101
=1-1/101=100/101

1/1*3+1/3*5+1/5*7......+1/99*101
=1/2(1-1/3+1/3-1/5+1/5-1/7+......+1/99-1/101)
=1/2(1-1/101)
=50/101

上过高中吗?这是典型的用裂项相消地方法解答的题目。
1/1x3+1/3x5+1/5x7........1/99x101
=1/2 *(1-1/3+1/3-1/5+1/5-1/7+。。。+1/99-1/101)
=1/2 (1-1/101)
=50/101

50/101

经典奥数题11/1x3+1/3x5+1/5x7.1/99x101解题思路请写清楚 因式分解:x5+x3+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 1/1x3+1/2x4+1/3x5+ 1/1x3+1/3x5+.+1/2005x2008 3x5/3-5/3x3/1 怎么简算 1x2+2x3+3x4+4x5+.+15x16 计算1x3+3x5+5x7+…+97x99 x5-x4+x3-x2+x-1因式分解 X5-X4+X3+X2+X+1因式分解 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 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 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 1、5/4x3+5/4 2、6/11x4/17+4/11x5/17 3、36x3/4-3÷4-3/4x3 4、23x(2/23+1/5)x5 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 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 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