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

If S=(1)/(1+1^(2)+1^(4))+(2)/(1+2^(2)+2^(4))+(3)/(1+3^(2)+3^(4))+......oo then find the value of 14S.

1+((log n)^(2))/(2!)+((Log n)^(4))/(4!)+...... oo =

If S=sum_(n=2)^(oo)(3n^(2)+1)/((n^(2)-1)^(3)) then (9)/(4S) is

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

If int_(log2)^(x)(dx)/(sqrt(e^(x)-1))=(pi)/(6), then x is equalto 4 (b) ln8(c)ln4(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

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

If log a=(1)/(2)log b=(1)/(5)log c then a^(4)b^(3)c^(-2)=

S_(n)=[(1)/(1+sqrt(n))+(1)/(2+sqrt(2n))+...+(1)/(n+sqrt(n^(2)))] then (lim_(n rarr oo)S_(n) is equal to (A)log2(B)log4 (C) log 8 (D) none of these