Prove that `lim_(n->oo)a_n=-1/4,` where `a_n=n^2,(sqrt(1+1/n)+sqrt(1-1/n)-2)` for `n in N *.`

lim_(n->oo)[1/sqrt(2n-1^2) +1/sqrt(4n-2^2)+1/sqrt(6n-3^2)+...+1/n]

Evaluate: lim_(n->oo)n^2{sqrt((1-cos(1/n))sqrt((1-cos(1/n)) sqrt((1-cos(1/n)) ..oo)))}dot

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

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

lim_(n rarr oo)(sqrt(n+1)-sqrt(n))=0

If a_1=1\ a n d\ a_(n+1)=(4+3a_n)/(3+2a_n),\ ngeq1\ a n d\ if\ (lim)_(n->oo)a_n=n then the value of a_n is sqrt(2) b. -sqrt(2) c. 2\ d. none of these

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

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

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

lim_(n rarr oo)(1+sqrt(n))/(1-sqrt(n))