由题写出An=n+1/(2^n )A1=1+1/2;A2=2+1/2^2可知前n项和为Sn=A1+A2+……+AnSn=1+1/2+2+1/2^2+3+1/2^3+……+n+1/2^n=1+2+3+……+n+1/2+1/2^2+1/2^3+……+1/2^n可看出为2个数列后,前部分为等差数列公式求和,后面为等比数列公式求和Sn=(1+n)*n/2+[(1/2)*(1-1/2^n)/(1-1/2)]=(1+n)*n/2+(1-1/2^n)=(n^2+n+2)/2-1/(2^n)