`lim_(n->oo)sum_(n=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)

The value of sum_(k=2)^(oo){Lt_(n rarr oo)sum_(r=1)^(n)((sqrt(n))/(sqrt(r)(k sqrt(n)-sqrt(r))^(2))}]}

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

The value of underset( n rarroo)(lim) underset(r=1)overset(r=4n)(sum)(sqrt(n))/(sqrt(r ) (3 sqrt(r)+4)sqrt(n)^(2)) is equal to

sum_(n=1)^(oo)(1)/(sqrt(n)+sqrt(n+1))

Evaluate : lim_(n to oo)[(sqrt(n))/((3+4sqrt(n))^(2))+(sqrt(n))/(sqrt(2)(3sqrt(2)+4sqrt(n))^(2))+(sqrt(n))/(sqrt(3)(3sqrt(3)+4sqrt(n))^(2))+.......+(1)/(49n)]

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

The value of lim_(n to oo)sum_(r=1)^(n)(1)/(n) sqrt(((n+r)/(n-r))) is :