Find the summation of HGP

we noe that..........

-(ln(1-x)=x+x^2/2+x^3/3............∞ ..............for-1<x<1
puttin x=1/2
-ln(1/2)=1/2+1/(2)^2(2)+1/(2^3)(3)...........( 1)

bt wat we wan is1+1/2+1/(2)^2(3)+1/(2)^3(4).....

so nw for equation 1 multiply throut by 2
u get (-2)ln(1/2)=1+1/(2)(2)+1/(2)^2(3)........

so ur anwer basically is
(-2)ln(1/2)

cheero~