设$\sum\limits_{n = 1}^\infty {n{a_n}} $收敛,记${t_n} = \sum\limits_{k = 1}^\infty {k{a_{n + k}}} $,证明:数列$\left\{ {{t_n}} \right\}$收敛并求其极限
注:请问这题可不可以用Abel变换和$\varepsilon - N$定义证明啊
时间: 2024-12-14 18:04:40
设$\sum\limits_{n = 1}^\infty {n{a_n}} $收敛,记${t_n} = \sum\limits_{k = 1}^\infty {k{a_{n + k}}} $,证明:数列$\left\{ {{t_n}} \right\}$收敛并求其极限
注:请问这题可不可以用Abel变换和$\varepsilon - N$定义证明啊