`lim_(x->oo){1/3+1/(3^2)+1/(3^3)+........1/(3^n)}=`

lim_(n rarr oo)(1+(1)/(3)+(1)/(3^(2))+.......+(1)/(3^(n-1)))/(1+(1)/(2)+(1)/(2^(2))+.....+(1)/(2^(n-1)))

lim_ (n rarr oo) (1+ (1) / (2) + (1) / (2 ^ (2)) + (1) / (2 ^ (3)) + ...... (1) / (2 ^ (n))) / (1+ (1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (3)) ...... (1) / (3 ^ (n)))

lim_ (x rarr oo) {(1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (3)) + ...... (. 1) / (3 ^ (n))} =

lim_(n->oo) (3^(1/2).3^(1/4).3^(1/8)...............3^(1/2^n))= (i) sqrt3 (ii) 3 (iii) log3 (iv) none of these

evaluate lim_ (n rarr oo) [(1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (2)) + ......... + (1) / (3 ^ (n))]

lim_(n rarr oo)((1)/(1.3)+(1)/(3.5)+.............+(1)/((2n-1)(2n+) 1)))

lim_(n rarr oo)(n^(2)(1^(3)+2^(3)+......+n^(3)))/((1^(2)+2^(2)+......+n^(2))^(2))

lim_(x->oo) [(1)/(1times2)+(1)/(2times3)+(1)/(3times4)+.....+(1)/(n(n+1))]

lim_(nto oo) {(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+...+(1)/(n+n)} is, equal to

Evaluate lim _( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +2 ^(3)) + (3 ^(2))/(n ^(3)+ 3 ^(3))+ .... + (4)/(9n)).