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

sum_(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to

sum_(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/sqrt(r(r+1))) is equal to

sum_(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to tan^(-1)(sqrt(n))-(pi)/(4)tan^(-1)(sqrt(n+1))-(pi)/(4)tan^(-1)(sqrt(n))(d)tan^(-1)(sqrt(n)+1)

The value of sum_(r=1)^(n)(1)/(sqrt(a+rx)+sqrt(a+(r-1)x)) is -

Let K=sum_(r=1)^(n)(1)/(r sqrt(r+1)+(r+1)sqrt(r)) and [x] denotes greatest integer function less than or equal to x then [K]

If lim_(n rarr oo)(sum_(r=1)^(n)sqrt(r)sum_(r=1)^(n)(1)/(sqrt(r)))/(sum_(r=1)^(n)r)=(k)/(3) then the value of k is

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

m sum_(r=1)^(n)(1)/(n)sqrt((n+r)/(n-r))

The summation of series sum_(r=1rarr99)(1)/(sqrt(r+1)+sqrt(r))is

sum_(r=1)^nsin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to (a) tan^(-1)(sqrt(n))-pi/4 (b) tan^(-1)(sqrt(n+1))-pi/4 (c) tan^(-1)(sqrt(n)) (d) tan^(-1)(sqrt(n)+1)