Find `lim_(n->oo)[(n^3+1)^(1/2)-n^(3/2)]-:n^(3/2)`

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)(2^(n)+3^(n))^(1/n)

lim_(nto oo)((1^(2))/(1-n^(3))+(2^(2))/(1-n^(3))+ . . . .+(n^(2))/(1-n^(3)))=

Find lim_ (n rarr oo) (n ^ (3) + a) (n + 1) ^ (3) a] ^ (- 1) (2 ^ (n + 1) + a) (2 ^ (n) + a) ^ (- 1)

A) |lim_(n rarr oo)((n^((1)/(2)))/(n^((3)/(2)))+(n^((1)/(2)))/((n+3)^((3)/(2)))+....+(n^((1)/(2)))/( n+3(n-1) ^((3)/(2))))=

Let a = lim_(n rarr oo) (1+2+3+.....+n)/(n^(2))= , b = lim_(n rarr oo) (1^(2)+2^(2)+.....+n^(2))/(n^(3))= then

Find lim_(n rarr oo)((1.3.5...(2n-1)}(n+1)^(4)]+[n^(4)(1.3.5...(2n-1)) (2n+1)]

Evaluate the following limit: (lim)_(n rarr oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))++(n-1)/(n^(2)))

Evaluate the following limit: (lim)_(n->oo)(1/(n^2)+2/(n^2)+3/(n^2)++(n-1)/(n^2\ ))

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