摘要：$$ \begin{aligned} &设a_0=1,a_1=2，\\ &且n(n+1)a_{n+1}=n(n-1)a_n-(n-2)a_{n-1},n=1,2,3,\cdots，\\ &求\cfrac{a_0}{a_1}+\cfrac{a_1}{a_2}+\cdots+\cfrac{a_{50}}{a_{51}}的值 \end{aligned} $$ 阅读全文

摘要：$$ \begin{aligned} &已知数列\{a_n\}满足a_1=2t-3(t\in \mathbb{R}且t\neq \pm 1),\\ &a_{n+1}=\cfrac{(2t^{n+1}-3)a_n+2(t-1)t^n-1}{a_n+2t^n-1}(n\in \mathbb{N}^*)\\ &(1)求数列\{a_n\}的通项公式。\\ &(2)若t>0，比较a_{n}与a_{n+1}的大小。\\ \end{aligned} $$ 阅读全文