已知数列an满足a1+2a2+3a3+……+nan=2^n,求an

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已知数列an满足a1+2a2+3a3+……+nan=2^n,求an

已知数列an满足a1+2a2+3a3+……+nan=2^n,求an
已知数列an满足a1+2a2+3a3+……+nan=2^n,求an

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

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)

a1+2a2+3a3+……+nan=2^n
a1+2a2+3a3+……+n-1an-1=2^n-1
nan=2^n-2^n-1=2^n-1
an=[2^n-1]/n

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