Find the value of
`underset(ntooo)lim[(1^(2))/(1^(3)+n^(3))+(2^(2))/(2^(3)+n^(3))+(3^(2))/(3^(3)+n^(3))+...+(n^(2))/(n^(3)+n^(3))]`

lim_(nrarroo) [(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+(3^(2))/(n^(3)+3^(3))+...+(1)/(2n)]

Evaluate : underset(n to oo) lim[((1+1^(2)/n^(2)))(1+(2^(2))/(n^(2)))(1+(3^(2))/(n^(2)))…(1+(n^(2))/(n^(2)))]^((1)/(n))

Evaluate : underset(nrarroo)"lim"(2n^(2)+3n-9)/(3n^(3)+2n+7)

Evaluate : underset(n to oo) lim[(1)/(n)+(1)/(n+1)+(1)/(n+2)+…+(1)/(3n)]

Find the value of underset(ntooo)lim[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

Evaluate : underset(nrarroo)"lim"(3n^(2)-4n+6)/(n^(2)+6n-7)

Evaluate : underset(n to oo) lim[(1+(1)/(n))(1+(2)/(n))(1+(3)/(n))…(1+(n)/(n))]^((1)/(n))

Find the values of the following limts : underset(nrarroo)"lim"(1^(2)+2^(2)+3^(2)+...+n^(2))/(n^(3))

The value of underset(n to oo)lim[(sqrt(n+1)+sqrt(n+2)+…+sqrt(2n-1))/(n^((3)/(2)))]

The value of lim_(n to oo) sum_(r=1)^(n)(r^(2))/(r^(3)+n^(3)) is -