Sn=1-1/2+1/3-1/4+...+1/(2n-1)-1/2n
=1+1/2+1/3+1/4+...+1/(2n-1)+1/2n-2(1/2+1/4+...+1/2n)
=1+1/2+1/3+1/4+..+1/(2n-1)+1/2n-(1+1/2+1/3+...+1/n)
=1/(n+1)+1/(n+2)+...+1/2n=Tn
∴Sn=Tn