maths SIMPLE problem plz do :)

1/2{1+1/2(1/2)+1/3(1/2)² +..................}

=1/2{1+(loge)²/2}

=1/2 +(loge)²/4

a question from board exam ap state board 2009

hyeh how u got the 2nd step log e which formula applied :(

i don know pp i will inform if i will know[4]

yeah i got it [4][4]

yaar deekh x =-1/2 put karo so

-ln(1-1/2)=1/2+1/2(1/2)+..................

add 1/2 to both side to get

1/2-ln(1-1/2)=1+1/2(1/2)+..................

ans will be
1/2(1/2-ln(1-1/2))

= 1/4-ln(1/2)/2

yup....