若数列{an}满足a1+3a2+3²a3+···+3^n-1an=n/2 则an=
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若数列{an}满足a1+3a2+3²a3+···+3^n-1an=n/2 则an=
![若数列{an}满足a1+3a2+3²a3+···+3^n-1an=n/2 则an=](/uploads/image/z/5304722-50-2.jpg?t=%E8%8B%A5%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%2B3a2%2B3%26sup2%3Ba3%2B%C2%B7%C2%B7%C2%B7%2B3%5En-1an%3Dn%2F2+%E5%88%99an%3D)
因为a1+3a2+3^2a3+···+3^(n-1)an=n/2,所以a1+3a2+3^2a3+···+3^(n-2)a(n-1)=(n-1)/2
两式相减即有3^(n-1)an=n/2-(n-1)/2,化简得:an=1/[2*3^(n-1)] (n∈N*)
两式相减即有3^(n-1)an=n/2-(n-1)/2,化简得:an=1/[2*3^(n-1)] (n∈N*)
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