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

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

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

lim_ (n rarr oo) ((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 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 rarr oo){(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+....+(1)/((2n+1)(2n+3 ))

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

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

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

lim_(n rarr oo)(5^((1)/(n))+3^(1/n)-1)^(n)