1/1×2+1/3×5+1/5×7+.+1/49×51=?

1/3+1/5+1/7+.+1/2n+1 1+3+5+7+.+（2n-1) (3+5/7-2/3)×(1/5+1/7+1/13)-(1/5-1/7+1/13)×3+(1/5+1/7+1/13)×(2/3-7/5)有一个打错了(3+5/7-2/3)×(1/5+1/7+1/13)-(1/5-1/7+1/13)×3+(1/5+1/7+1/13)×(2/3-7/5) 矩阵特征值问题,怎样让矩阵的特征值变小1 3 3 3 5 5 7 7 7 9;1/3 1 2 3 4 4 5 5 6 8;1/3 1/2 1 2 4 5 6 5 7 7;1/3 1/3 1/3 1/2 4 5 6 7 8 7;1/5 1/4 1/4 1/4 1 3 5 5 6 7;1/5 1/4 1/5 1/5 1/3 1 3 3 1 5;1/7 1/5 1/6 1/6 1/5 1/3 1 1 3 7;1/7 1/5 1/5 1-3+5-7+... 1/3 1/2 5/11 7/18 1/3 1/1*3=1/2（1-1/3）1/3*5=1/2（1/3-1/5）1/5*7=1/2（1/5-1/7）.1/17*19=1/2（1/17-1/19）所以1/1*3+1/3*5+1/5*7+.1/17*19=1/2（1-1/3）+1/2（1/3+1/5）+1/2（1/5-1/7）+.1/2（1/17-1/19）=1/2（1-1/3+1/3-1/5+1/5-1/7+1/7.+1/17-1/19）=1/2（1-1/1 ((1/2)-1)*((1/3)-1)*((1/4)-1)*((1/5)-1)*((1/6)-1)*((1/7)-1)*((1/8)-1)*((1/9)-1)*((1/10)-1) 因为1/1*3=1/2*（1-1/3）,1/3*5=1/2*(1/3-1/5),1/5*7=1/2*(1/5-1/7),.,1/17*19=1/2*(1/17-1/19)所以1/1*3+1/3*5+1/5*7+...+1/17*19=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+...+1/2*(1/17-1/19)=1/2*(1-1/3+1/3-1/5+1/5-1/7+...+1/17-1/19)=1/2*(1-1/19)=9/19(1 用Matlab用计算特征值和特征向量1 1/7 1/5 1/3 1/5 1/67 1 7/5 7/3 7/5 7/65 5/7 1 5/3 5/8 5/63 3/7 3/5 1 3/5 1/25 5/7 8/5 5/3 1 5/66 6/7 6/5 2 6/5 1 (1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7) 简算(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7) 简便计算 matlab 编程数组的数据如下：8 1 1 1 1 1 1 3 3 2 1 1 5 1 1 3 1 1 2 1 1 5 3 3 3 1 1 4 5 1 1 1 1 1 2 2 2 2 4 3 1 5 4 2 1 1 1 2 1 3 1 1 2 2 5 2 1 3 2 5 1 1 3 1 1 1 1 2 1 5 4 2 2 1 3 4 1 2 3 1 2 4 4 1 1 1 2 2 2 2 2 1 1 4 4 1 3 2 1 1 5 1 1 3 7 1 1 求证1/(2*3)+1/(3*5)+1/(4*7)+...+1/((n+1)(2n+1)) 1/2+1/3+1/4+1/5+1/6+1/7+.1/20= 求矩阵最大特征根特征向量[1 5/7 5/6 5 5/27/5 1 6/7 7 7/26/5 6/7 1 6 31/5 1/7 1/6 1 1/22/5 2/7 1/3 2][1 5/7 5/6 5 5/2 7/5 1 6/7 7 7/26/5 6/7 1 6 31/5 1/7 1/6 1 1/22/5 2/7 1/3 2 1] (1+1/2)*(1+1/4)*(1+1/6)*.*(1+1/20)*(1-1/3)*(1-1/5)+(1-1/7)*.*(1-1/2 求和：-1+3-5+7-...+（-1)^n(2n-1) 5x+1/2-1=7x-1/3