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" The determinant "|[a,a+d,a+2d],[a^(2),...

" The determinant "|[a,a+d,a+2d],[a^(2),(a+d)^(2),(a+2d)^(2)],[2a+3d,2(a+d),2a+d]|=0

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The determinant : |{:(a,a+d,a+2d),(a^2,(a+d)^2,(a+2d)^2),(2a+3d,2(a+b),2a+d):}|=0 Then

If |(a,a +d,a +2d),(a^(2),(a + d)^(2),(a + 2d)^(2)),(2a + 3d,2 (a +d),2a +d)| = 0 , then

If |(a,a +d,a +2d),(a^(2),(a + d)^(2),(a + 2d)^(2)),(2a + 3d,2 (a +d),2a +d)| = 0 , then

let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d)),1/( (a + d) (a +2d))],[1/(a+ d),1/( (a+ d) (a + 2d)), 1/((a+2d) (a + 3d))],[1/(a +2d), 1/((a + 2d) (a +3d)), 1/((a+3d) (a + 4d))]|

let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d)),1/( (a + d) (a +2d))],[1/(a+ d),1/( (a+ d) (a + 2d)), 1/((a+2d) (a + 3d))],[1/(a +2d), 1/((a + 2d) (a +3d)), 1/((a+3d) (a + 4d))]|

let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d)),1/( (a + d) (a +2d))],[1/(a+ d),1/( (a+ d) (a + 2d)), 1/((a+2d) (a + 3d))],[1/(a +2d), 1/((a + 2d) (a +3d)), 1/((a+3d) (a + 4d))]|

let a>0,d>0 find the value of the determinant (1)/(a)_((1)/(a(a+d))),(1)/((a+d)(a+2d))(1)/(a+d),(1)/((a+d)(a+2d)),(1)/((a+2d)(a+3d))(1)/(a+2d),(1)/((a+2d)(a+3d)),(1)/((a+3d)(a+4d))]|

The mean of the series a,a+d, a+2d,…,a+2nd is

The mean of the series a, a + d, a + 2d, …, a + 2 nd, is