`(sqrtm+sqrtn)(sqrtm+sqrtn)`

The value of : lim_(ntooo)((1)/(sqrtn sqrt(n+1))+(1)/(sqrtn sqrt(n+2))+ (1)/(sqrtn sqrt(n +3)) + ...... +(1)/(sqrtn sqrt(2n))) is:

Let S=Sigma_(n=1)^(999) (1)/((sqrt(n)+sqrt(n+1))(4sqrt(n)+4sqrtn+1)) , then S equals ___________.

Let S=(sqrt(1))/(1+sqrt1+sqrt(2))+sqrt(2)/(1+sqrt(2)+sqrt(3))+(sqrt(3))/(1+sqrt(3)+sqrt(4))+...+(sqrt(n))/(1+sqrt(n)+(sqrtn+1))=10 Then find the value of n.

If f(x) is continuous in [0, 1] and f((1)/(3))=12 , then the value of lim_(nrarroo)f((sqrtn)/(3sqrtn+1)) is equal to

Statement-1: For every natural number n ge 2, (1)/(sqrt1)+(1)/(sqrt2)+…..(1)/(sqrtn) gt sqrtn Statement-2: For every natural number n ge 2, sqrt(n(n+1) lt n+1

If cos3 6^(@)+cot(7 1/2@)=sqrt(n_1)+sqrt(n_2)+sqrt(n_3)+sqrt(n_1)+sqrt(n_5)+sqrtn_6, then the value of sum_(i=1)^6 n_i^2 must be

underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)/(n)]

If 3 log sqrtm + 2 log ""^(3) sqrtn = 1. find the value of m^(9) n^(4) .

If 1/(sqrt(2011+sqrt(2011^2-1)))=sqrtm-sqrtn where m and n are positive integers , what is the value of m + n.

Prove that 1+(1)/(sqrt2)+(1)/(sqrt3)+....+(1)/(sqrtn) ge sqrtn, AA n in N