已知数列{an}满足:a1+8/7*a2+(8/7)²*a3+...(8/7)^(n-1)an=n(n+1),
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已知数列{an}满足:a1+8/7*a2+(8/7)²*a3+...(8/7)^(n-1)an=n(n+1),n∈N+,求an
{a1+8/7*a2+(8/7)²*a3+...(8/7)^(n-1)an}-{a1+8/7*a2+(8/7)²*a3+...(8/7)^(n-2)a(n-1)}=n(n+1)-(n-1)n=2n
即有(8/7)^(n-1)an=2n
an=2n(7/8)^(n-1)
即有(8/7)^(n-1)an=2n
an=2n(7/8)^(n-1)
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