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

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

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))]|

lim_(x rarr oo)(1)/(1+n sin^(2)nx)is equal to -1 (b) 0 (c) 1 (d) oo

If f(x)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a)-1 (b). 1 ( c.) 0 (d).2

lim_ (n rarr oo) int_ (0) ^ (2) (1+ (t) / (n + 1)) ^ (n) d

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

The sequence (:a_(n-1):),n in N is an arithmetical progression and d is its common difference.If lim_(n rarr oo)(1-(d^(2))/(a_(1)^(2)))(1-(d^(2))/(a_(2)^(2)))cdots cdots(1-(d^(2))/(a_(n)^(2))) converges to (1)/(4) and a_(1)=8 then find the value of d

lim_(x rarr oo)(x(log x)^(3))/(1+x+x^(2)) equal 0(b)-1(c)1(d) none of these