线性代数提高线性代数随机推荐线性代数做题本（一）解答版解答题矩阵运算不看本题本题讨论已掌握查看解析收入错题#8587设数列 {an},{bn}\left\{ {a}_{n}\right\},\left\{ {b}_{n}\right\}{an},{bn} 满足 (anbn)=(12−14)(an−1bn−1)(n=1,2,⋯),a0=1,b0=−1\left(\begin{array}{l} {a}_{n} \\ {b}_{n} \end{array}\right) = \left(\begin{array}{rr} 1 & 2 \\ - 1 & 4 \end{array}\right) \left(\begin{array}{l} {a}_{n - 1} \\ {b}_{n - 1} \end{array}\right) \left({n = 1,2,\cdots }\right),{a}_{0} = 1,{b}_{0} = - 1(anbn)=(1−124)(an−1bn−1)(n=1,2,⋯),a0=1,b0=−1,求级数 ∑n=0∞1an−bn\mathop{\sum }\limits_{n = 0}^{\infty }\frac{1}{{a}_{n} - {b}_{n}}n=0∑∞an−bn1 的和.