设数列{An}满足A1+3A2+3²A3+…+3n-1An=3/n.(1)求数列{An}的通项.

设数列{An}满足A1+3A2+3²A3+…+3n-1An=3/n.(1)求数列{An}的通项.
设数列{An}满足A1+3A2+3²A3+…+3n-1An=3/n.(1)求数列{An}的通项.

设数列{An}满足A1+3A2+3²A3+…+3n-1An=3/n.(1)求数列{An}的通项.
解a1+3a2+3^2a3+3^3a4+.+3^(n-2)a(n-1)+3^(n-1)an=n/3
a1+3a2+3^2a3+3^3a4+.+3^(n-2)a(n-1)=(n-1)/3
两式相减,得
3^(n-1)an=n/3-(n-1)/3=1/3
an=(1/3)/3^(n-1)=1/(3^n)