已知数列(an)满足a1=2a,an=2a-An-1分之a的平方(n大于等于2),其中a是不为0的常数,令bn=an-a分之1求证:数列(bn)是等数数列; 求数列(an)的通项公式?
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![已知数列(an)满足a1=2a,an=2a-An-1分之a的平方(n大于等于2),其中a是不为0的常数,令bn=an-a分之1求证:数列(bn)是等数数列; 求数列(an)的通项公式?](/uploads/image/z/8825889-57-9.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%BC%88an%EF%BC%89%E6%BB%A1%E8%B6%B3a1%3D2a%2Can%3D2a-An-1%E5%88%86%E4%B9%8Ba%E7%9A%84%E5%B9%B3%E6%96%B9%EF%BC%88n%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E2%EF%BC%89%2C%E5%85%B6%E4%B8%ADa%E6%98%AF%E4%B8%8D%E4%B8%BA0%E7%9A%84%E5%B8%B8%E6%95%B0%2C%E4%BB%A4bn%3Dan-a%E5%88%86%E4%B9%8B1%E6%B1%82%E8%AF%81%EF%BC%9A%E6%95%B0%E5%88%97%28bn%29%E6%98%AF%E7%AD%89%E6%95%B0%E6%95%B0%E5%88%97%EF%BC%9B+++++%E6%B1%82%E6%95%B0%E5%88%97%28an%29%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%3F)
已知数列(an)满足a1=2a,an=2a-An-1分之a的平方(n大于等于2),其中a是不为0的常数,令bn=an-a分之1求证:数列(bn)是等数数列; 求数列(an)的通项公式?
已知数列(an)满足a1=2a,an=2a-An-1分之a的平方(n大于等于2),其中a是不为0的常数,令bn=an-a分之1
求证:数列(bn)是等数数列; 求数列(an)的通项公式?
已知数列(an)满足a1=2a,an=2a-An-1分之a的平方(n大于等于2),其中a是不为0的常数,令bn=an-a分之1求证:数列(bn)是等数数列; 求数列(an)的通项公式?
An-a=-(An-1-a),所以An=(-1)的n-1次方xa+a,Bn=(-1)的n-1次方xa,所以bn等比数列,
这类题目可以用待定系数法的,配成,(An+b)=cx(An-1+b),再分解求出b,c
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