(i) `((root(n)(a))^(sqrt(n)))^(sqrt(n))`

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)]

For all n in N,1+(1)/(sqrt(2))+(1)/(sqrt(3))+(1)/(sqrt(4))++(1)/(sqrt(n))

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

Let T_(n)=(1)/((sqrt(n)+sqrt(n+1))(4sqrt(n)+4sqrt(n+1))) and S_(n)=sum_(r=1)^(n)T_(r) then find S_(15) .

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

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

The sum of the infinte series sin^(-1)((1)/(sqrt(2)))+sin^(-1)((sqrt(2)-1)/(sqrt(6)))+...sin^(-1)((sqrt(n)-sqrt(n-1))/(sqrt(n(n+1))))

lim_ (n-> oo) (sqrt (n))/(sqrt (n)+sqrt (n+1)) = (i) 1 (ii) 1/2 (iii) 0 (iv) infty

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