已知数列{an}的通项公式为an=n/2^n,则此数列的前n项和Sn=
问题描述:
已知数列{an}的通项公式为an=n/2^n,则此数列的前n项和Sn=
答
a1=1/2 a2=2/4 a3=3/8 ……an=n/2^nSn=1/2+2/4+3/8+……+n/2^nSn/2=1/4+2/8+3/16+……+(n-1)/2^n+n/2^(n+1)Sn-Sn/2=1/2+1/4+1/8+……+1/2^n-n/2^(n+1)=(1/2-1/2^n*1/2)/1-1/2)-n/2^(n+1)=1-1/2^n-n/2^(n+1)...