If `S=1/2(1/2+1/3)-1/4(1/(2^2)+1/(3^2))+1/6(1/(2^3)+1/(3^3))..........` then `S=`

1/2(1/2+1/3)-1/4(1)/(2^(2))+(1)/(3^(2))+1/6(1)/(2^(3))+(1)/(3^(3))+…infty is equal to

1/2(1/2+1/3)-1/4((1)/(2^(2))+(1)/(3^(2)))+1/6((1)/(2^(3))+(1)/(3^(3)))+…infty is equal to

Sum of the series (1)/(2)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2^(2))+(1)/(3^(2)))+(1)/(6)((1)/(2^(3))+(1)/(3^(3)))-... is

Sum of the series (1)/(2)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2^(2))+(1)/(3^(2)))+(1)/(6)((1)/(2^(3))+(1)/(3^(3)))+...oo

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.

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 (1)/(1^(3))+(1+2)/(1^(3)+2^(3))+(1+2+3)/(1^(3)+2^(3)+3^(3))+......n terms then lim_(n rarr oo)[S_(n)]