`lim_(x->oo){1/(a(a+d))+1/((a+d)(a+2d))+1/((a+2d)(a+3d))+..............to n terms}`

if quad (1)/(4)(3+d)+(1)/(4^(2))(3+2d)+.............oo=8 then the value of d is

(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))

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))]|

Show that Lt_(ntooo)[1/(a(a+d))+1/((a+d)(a+2d))+...+1/([a+(n-1)d][a+nd])]=1/(a.d) where a and d are constants. Hence find Lt_(ntooo)[1/1.4+1/4.7+...+1/((3n-1)(3n+2))]

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))]|

("lim")_(xtooo)1/(1+nsin^2n x)is equal (a)-1 (b) 0 (c) 1 (d) oo

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