已知数列an满足a1+2a2+3a3+……+nan=2^n,求an

问题描述:

已知数列an满足a1+2a2+3a3+……+nan=2^n,求an

a1+2a2+3a3+……+(n-1)a(n-1)+nan=2^n
a1+2a2+3a3+……+(n-1)a(n-1)=2^(n-1)
两式相减得
nan=2^n-2^(n-1)
nan=2^(n-1)
an=2^(n-1)/n