`(2n)/(n-3) + 1/(2n+3) + (3n+9)/((n-3)(2n+3)) = 0`

Evaluate lim _( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +2 ^(3)) + (3 ^(2))/(n ^(3)+ 3 ^(3))+ .... + (4)/(9n)).

lim_ (n rarr oo n rarr oo n pto n terms) (n) / ((n + 1) sqrt (2n + 1)) + (n) / ((n + 2) sqrt (2 (2n + 2)) ) + (n) / ((n + 3) sqrt (3 (2n + 3)) + dots)

If ((2n)!)/(3!(2n-3)!) and (n!)/(2!(n-2)!) are in the ratio 44:3 find n.

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

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

Prove that lim_ (n rarr oo) ((1 ^ (2)) / (n ^ (3)) + (2 ^ (2)) / (n ^ (3)) + (3 ^ (2)) / ( n ^ (3)) + .... + (n ^ (2)) / (n ^ (3))) = (1) / (3)

(lim)_(n->oo){1/(2n+1)+1/(2n+2)++1/(2n+n)} I n\ (1/3) b. I n\ (2/3) c. I n\ (3/2) d. I n\ (4/3)

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))))=

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