Lt[(1^(3))/(n^(4)+1^(4))+(2^(3))/(n^(4)+2^(4))+......+(1)/(2n)]=

Lt_(ntooo)[(1^(3))/(n^(4)+1^(4))+(2^(3))/(n^(4)+2^(4))+.........+(1)/(2n)]=

Lt_(n rarr oo)[(1^(3))/(n^(4)+1^(4))+(2^(3))/(n^(4) + 2^(4))+....+(n^(3))/(n^(4)+n^(4))]

lim_ (n rarr oo) [(1 ^ (3)) / (n ^ (4) + 1 ^ (4)) + (2 ^ (3)) / (n ^ (4) + 2 ^ (4)) ++ (1) / (2n)] =

Lt_(ntooo)[(1)/(1+n^(3))+(4)/(8+n^(3))+(9)/(27+n^(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

lm_ (n rarr oo) ((1 ^ (3)) / (n ^ (4)) + (2 ^ (4)) / (n ^ (4)) + (3 ^ (3)) / (n ^ (4)) + ...... + (n ^ (3)) / (n ^ (4)))

For n in N , (4-(2)/(1))(4-(2)/(2))(4-(2)/(3))(4-(2)/(4)).........(4-(2)/(n)) is

4C_(0)+(4^(2))/(2)*c_(1)+(4^(3))/(3)c_(2)+............+(4^(n+1))/(n+1)C_(n)=(5^(n+1)-1)/(n+1)

{:(" "Lt),(n rarr oo):} ((1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-2^(2)))+....+(1)/(sqrt(3n^(2))))=