Question

已知数列{an}满足a1+a2/2+...=2n-1

设数列{an}满足:a1+a2/2+a3/3+...+an/n=a^2n-1（a大于0,a≠1,n∈N+),1.求an 2.求{an}的前几项和Sn

Answer 1

设Tn=a1+a2/2+a3/3+...+an/n=a^2n-1,①,Tn-1=a1+a2/2+a3/3+...+an-1/(n-1)=a^2n-3,②,①-②得：an/n=Tn-Tn-1=a^(2n-1)-a^(2n-3)=(a��-1)a^(2n-3),所以an=n(a��-1)a^(2n-3),