Prove that `sqrt(C_1) +sqrt(C_2) +sqrt(C_3)+...+sqrt(C_n)le 2^(n-1) +(n-1)/2`

If C_(r ) = (n!)/(r!(n - r)!) , then prove that sqrt(C_(1)) + sqrt(C_(2)) + …. + sqrt(C_(n)) sqrt(n(2^(n) - 1))

If C_(r ) = (n!)/(r!(n - r)!) , then prove that sqrt(C_(1)) + sqrt(C_(2)) + …. + sqrt(C_(n)) sqrt(n(2^(n) - 1))

If C_r=(n !)/([r !(n-r)]), the prove that sqrt(C_1)+sqrt(C_2)+.......sqrt(C_n) lt sqrt(n(2^n-1)) ="">

If C_r=(n !)/([r !(n-r)]), the prove that sqrt(C_1)+sqrt(C_2)+.......sqrt(C_n) lt sqrt(n(2^n-1)) ="">

Prove that nC_1(nC_2)^2(n C_3)^3.......(n C_n)^n le ((2^n)/(n+1))^((n+1)C_2),AAn in Ndot

If a_(1),a_(2),a_(3)... are in A.P then prove that (1)/(sqrt(a)_(1)+sqrt(a)_(2))(+)/(sqrt(a)_(2)+sqrt(a)_(3))+...+(1)/(sqrt(a)_(n-1)+sqrt(a)_(n))=(n-1)/(sqrt(a)_(n)+sqrt(a)_(1))

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

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

The sum n terms of the series 1/(sqrt(1)+sqrt(3))+1/(sqrt(3)+sqrt(5))+1/(sqrt(5)+sqrt(7))+ is sqrt(2n+1) (b) 1/2sqrt(2n+1) (c) 1/2sqrt(2n+1)-1 (d) 1/2{sqrt(2n+1)-1}

The sum n terms of the series (1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))+(1)/(sqrt(5)+sqrt(7))+... is sqrt(2n+1) (b) (1)/(2)sqrt(2n+1)(c)(1)/(2)sqrt(2n+1)-1(d)(1)/(2){sqrt(2n+1)-1}