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Find the sum of series of form 1/(a(a+d)...

Find the sum of series of form `1/(a(a+d))+1/((a+d)(a+2d))+1/((a+2d)(a+3d))+..........1/((a+(n-2)d)(a+(n-1)d))`

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(ii) sum of series of form (1)/(a(a+d))+(1)/((a+d)(a+2d))+(1)/((a+2d)(a+3d))+......(1)/((a+(n-2)d)(a+(n-1)d))

lim_(x rarr oo){(1)/(a(a+d))+(1)/((a+d)(a+2d))+(1)/((a+2d)(a+3d))+............ nterms

Lt_(x to oo) ((1)/(a(a+d))+(1)/((a+d)(a+2d))+.....+(1)/([a+(n-1)d][a+nd]))=

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))]|

a+(a+d)+(a+2d)+....+[a+(n-1)d]=(n)/(2)(2a+(n-1)d)

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))]|

Prove that a+(a+d)+(a+2d)+........n "terms"=n/2(2a+(n-1)d)