Evaluate :
`lim_( n -> 0 ) ( 2^n -1 ) / (( 1 + n )^(1/2 ) -1 )`

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

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

Using Sandwich theorem, evaluate lim_ (n rarr oo) ((1) / (1 + n ^ (2)) + (1) / (2 + n ^ (2)) + ...... + (n) / (n + n ^ (2)))

Find : lim_( n rarr oo) (2^(1/n - 1 )/ ( 2^(1/n) +1 ) ) (a) 1 (b) 1/2 (c) -1 (d) 0

Evaluate lim_ (n rarr oo) (1) / (n) sum_ (r = n + 1) ^ (2n) log_ (e) (1+ (r) / (n))

Evaluate lim_ (n rarr oo) [(1+ (1) / (n)) 91+ (2) / (n)) .... (1+ (n) / (n))] ^ ((1) /(a))

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

Evalute lim_ (n rarr oo) [(1) / ((n + 1) (n + 2)) + (1) / ((n + 2) (n + 4)) + ...... + ( 1) / (6n ^ (2))]

Evaluate: lim_(nrarr0) (((2n)!)/(n!n^(n)))^(1/n)

Evaluate :lim_(n rarr oo)sum_(r=1)^(n)(1)/((n^(2)+r^(2))^(1/2))