If `S=(1/2)^2+((1/2)^2 1)/3+((1/2)^3 1)/4+((1/2)^4 1)/5+...... ,t h e n` (a)`S=ln8-2` (b) `S=ln(4/e)` (c)`S=ln4+1` (d) none of these

S=((1)/(2))^(2)+(((1)/(2))^(2)1)/(3)+(((1)/(2))^(3)1)/(4)+(((1)/(2))^(4)1)/(5)+......, then (a)S=ln8-2( b) S=ln((4)/(e))(c)S=ln4+1(d) none of these

If (log)_e4-1. 3868 ,t h e n(log)_e 4.01= 1.3968 (b) 1.3898 (c) 1.3893 (d) none of these

If S={x in N :2+(log)_2sqrt(x+1)>1-(log)_(1/2)sqrt(4-x^2)} , then (a)S={1} (b) S=Z (c) S=N (d) none of these

If S={x in N :2+(log)_2sqrt(x+1)>1-(log)_(1/2)sqrt(4-x^2)} , then (a) S={1} (b) S=Z (d) S=N (d) none of these

IfS_n=[1/(1+sqrt(n))+1/(2+sqrt(2n))++1/(n+sqrt(n^2))],t h e n(lim)_(n rarr oo)S_n is equal to (a)log 2 (b) log4 (c)log 8 (d) none of these

If S={x in N :2+(log)_2sqrt(x+1)>1-(log)_(1/2)sqrt(4-x^2)} , then S={1} (b) S=Z (d) S=N (d) none of these

If (log)_e4=1. 3868 , then (log)_e 4.01= (a) 1.3968 (b) 1.3898 (c) 1.3893 (d) none of these

If (log)_e4=1. 3868 , then (log)_e 4.01= (a) 1.3968 (b) 1.3898 (c) 1.3893 (d) none of these

The sum of the series: 1/((log)_2 4)+1/((log)_4 4)+1/((log)_8 4)++1/((log)_(2n)4) is (n(n+1))/2 (b) (n(n+1)(2n+1))/(12) (c) (n(n+1))/4 (d) none of these

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these