(i) `lim_(n->00) (sqrt (n+1)-sqrtn)`=0

lim_(n rarr oo)n[sqrt(n+1)-sqrt(n))]

lim_(n->oo) nsin(1/n)

lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

The value of lim_(n->oo)(sqrt(1)+sqrt(2)+sqrt(3)+.....+sqrt(n))/(nsqrt(n)) is

lim_(n rarr oo)(3+sqrt(n))/(sqrt(n))

lim_(n to oo)[(sqrt(n+1)+sqrt(n+2)+....+sqrt(2n))/(n sqrt((n)))]

The value of lim_(xrarroo)(sqrt(n^2+1)+sqrt(n))/((n^4+n)^(1/4)+4sqrt(n)) , is

The value of lim_(nto oo)(sqrt(n^(2)+n+1)-[sqrt(n^(2)+n+1)]) where [.] denotes the greatest integer function is

The value of : lim_(ntooo)((1)/(sqrtn sqrt(n+1))+(1)/(sqrtn sqrt(n+2))+ (1)/(sqrtn sqrt(n +3)) + ...... +(1)/(sqrtn sqrt(2n))) is:

underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)/(n)]