[" 15."lim_(x rarr oo)sum_(r=1)^(oo)(sqrt(n))/(sqrt(r)(3sqrt(r)+4sqrt(n))^(2))],[[" 1) "(1)/(35)," 2) "(1)/(14)]]

lim_(n->oo)sum_(r=1)^n(sqrt(n))/(sqrt(r)(3sqrt(r)+4sqrt(n))^2)

The value of lim_(n rarr oo)sum_(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+sqrt(n))^(2)) is equal to (1)/(35) (b) (1)/(4)(c)(1)/(10) (d) (1)/(5)

lim_ (n rarr oo) sum_ (n = 1) ^ (n) (sqrt (n)) / (sqrt (r) (3sqrt (r) + 4sqrt (n)) ^ (2))

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

The value of ("lim")_(n rarr oo)sum_(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+sqrt(n))^2) is equal to

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

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

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