已知数列an满足1/a1a2+1/a2a3+……1/an-1an=(n-1)/a1an,求证为等差数列
问题描述：
已知数列an满足1/a1a2+1/a2a3+……1/an-1an=(n-1)/a1an,求证为等差数列
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答
1/(a1a2)+1/(a2a3)+……+1/(aan)=(n-1)/(a1an),①以n+1代n,得1/(a1a2)+1/(a2a3)+……+1/(aan)+1/(ana)=n/(a1a),②②-①,1/(ana)=n/(a1a)-(n-1)/(a1an),去分母得a1=nan-(n-1)a,∴an-a1=(n-1)(a-an),∴a-an=（an-a1)/(...