Show that :

`lim_( n -> oo ) ( b/n ) = 0`

lim_(n rarr oo)(pi n)^(2/n) =

Show that, lim_(n to oo)((1)/(n + 1)+(1)/(n+2)+…+(1)/(6n))=log 6 .

lim_ (n rarr oo) (x ^ (n)) / (n!)

Show that lim_(n rarr oo)((1)/(n+1)+(1)/(n+2)+...+(1)/(6n))=log6

lim_(n rarr oo) (1)/(n)= ________.

Statement [lim_ (n rarr oo) a_ (n)] = lim_ (n rarr oo) [a_ (n).] Denotes the greatestinteger function. Statement II lim_ (n rarr oo) a_ (n) = 3

If 0 lt alpha lt beta then lim_(n to oo) (beta^(n) + alpha^(n))^((1)/(n)) is equal to

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) sqrt(n)/sqrt(n+1)=

lim_(n rarr oo)tan^-1n/n