`lim_(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))+....+(r^(2))/(r^(3)+n^(3))+....+(1)/(2n))`

Evaluate: lim_(n rarr oo)((1^(2))/(n^(3))+(2^(2))/(n^(3))+(3^(2))/(n^(4))+...+(1)/(n))

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

lim_(n rarr oo)(1)/(n^(4))sum_(r=1)^(n)r^(3)=

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

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

lim_ (n rarr 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)(((n+1)^(1/3))/(n^(4/3))+((n+2)^(1/3))/(n^(4/3))+.....+((2n)^(1/3))/(n^(4/3))) is equal to

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