" 31."int_(n rarr oo)(n)/((n+1)sqrt((2n+1)))+(n)/((n+2)sqrt(2(2n+2)))+(n)/((n+3)sqrt(3(2n+3)))quad " up to n terms "

lim_ (n rarr oo n rarr oo n pto n terms) (n) / ((n + 1) sqrt (2n + 1)) + (n) / ((n + 2) sqrt (2 (2n + 2)) ) + (n) / ((n + 3) sqrt (3 (2n + 3)) + dots)

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

lim_(n rarr oo)(1)/(sqrt(n)sqrt(n+1))+(1)/(sqrt(n)sqrt(n+2))+......+(1)/(sqrt(n)sqrt(4n))

lim_(n rarr oo) n(sqrt(n^(2)+8)-n) =

lim_(n rarr oo) n(sqrt(n^(2)+6)-n) =

lim_(n rarr oo)(sin(1)/(sqrt((n))))((1)/(sqrt(n+1)))^(+(1)/(sqrt(n+2))+(1)/(sqrt(n+2)))

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

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