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

Evaluate the following limits: lim_(x to oo) ((1)/(3)+(1)/(3^(2))+....+(1)/(3^(n)))

the value of lim_(n->oo) {1/(n^3+1)+4/(n^3+1)+9/(n^3+1)+.................+n^2/(n^3+1)}

lim_(n->oo) {1/1.3+1/3.5+1/5.7+.....+1/((2n+1)(2n+3)) is equal to

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/n+1/(n+1)+1/(n+2)+…..+1/(3n)} =

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_(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))]

Evaluate lim_(n->oo)[1^2/(n^3+1^3) + 2^2/(n^3+2^3) +3^2/(n^3+3^3)+…+1/(2n)]

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