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职教组卷
  • 题型:解答题 题类:月考试卷 难易度:较难

    已知数列\(\{ a_{n}\}{,}\{ b_{n}\}\)满足\(a_{1}{=}\dfrac{1}{4}{,}a_{n}{+}b_{n}{=}1{,}b_{n{+}1}{=}\dfrac{b_{n}}{1{-}a_{n}^{2}}\).
    \((1)\)求\(b_{1}{,}b_{2}{,}b_{3}{,}b_{4}\);
    \((2)\)求证:数列\(\{\dfrac{1}{b_{n}{-}1}\}\)是等差数列,并求出数列\(\{ b_{n}\}\)通项公式;
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