Evaluate :
`lim_( n -> oo ) ( 3^n - 2^n ) / ( 3^n + 2^n )`

Evaluate: lim_ (n rarr oo) (1 ^ (4) + 2 ^ (4) + 3 ^ (4) + ... + n ^ (4)) / (n ^ (5)) - lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + ... + n ^ (3)) / (n ^ (5))

Evaluate: lim_ (n rarr oo) (1 ^ (4) + 2 ^ (4) + 3 ^ (4) + ... + n ^ (4)) / (n ^ (5)) - lim_ (n rarr oo) (1 ^ (3) + 2 ^ (3) + ... + n ^ (3)) / (n ^ (5))

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

Consider the following statements : I. lim_(n to oo) ( 2^n +(-2)^n)/(2^n) dos not exist II. lim_(n to oo) ( 3^n +(-3)^n)/(2^n) does not exist then

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

Find lim_ (n rarr oo) (4n ^ (2) + 6n + 2) / (4) n ^ (2)

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

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

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