设数列{an}对所有正整数n都满足:a1+2a2+2^2a3+…+2^(n-1)an=8-5n,求数列{an}的前n项和Sn

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设数列{an}对所有正整数n都满足:a1+2a2+2^2a3+…+2^(n-1)an=8-5n,求数列{an}的前n项和Sn设数列{an}对所有正整数n都满足:a1+2a2+2^2a3+…+2^(n-

设数列{an}对所有正整数n都满足:a1+2a2+2^2a3+…+2^(n-1)an=8-5n,求数列{an}的前n项和Sn
设数列{an}对所有正整数n都满足:a1+2a2+2^2a3+…+2^(n-1)an=8-5n,求数列{an}的前n项和Sn

设数列{an}对所有正整数n都满足:a1+2a2+2^2a3+…+2^(n-1)an=8-5n,求数列{an}的前n项和Sn
由:a1+2a2+2^2a3+…+2^(n-1)an=8-5n--------------------------------①
知:a1+2a2+2^2a3+…+2^(n-2)a(n-1)=8-5(n-1)-----------------------②
①-②得:2^(n-1)an=-5 n≥2
∴ an=-5*(1/2)^(n-1) n≥2
a1=8-5=3
∴S1=a1=3
Sn=a1+(a2+.+an)
=3-5×[1/2+.+(1/2)^(n-1)]
=3-5×[1-(1/2)^(n-1)] n≥2

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