a1=1/2a2=2/2^2a3=3/2^3.an=n/2^nSn=1/2+2/2^2+3/2^3+.+n/2^n1/2Sn=1/2^2+2/2^3+3/2^4+.+(n-1)/2^n+n/2^(n+1)Sn-1/2Sn=1/2+1/2^2+1/2^3+1/2^4+.1/2^2-n/2^(n+1)=1/2*[1-(1/2)^n]/(1-1/2)-n/2^(n+1)=1-(1/2)^n-n/2^(n...