What is this series? What is its analytical solution?
$$x_{n+1}=\frac{A+Bx_{n}}{C+Dx_{n}}$$
This can also be written as:
$$x_{n+1}=\frac{B}{D}+\frac{A-\frac{BC}{D}}{C+Dx_{n}}$$
2026-04-06 00:14:17.1775434457
Identify a number series
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In my answer to this question, I detailed the steps for solving a first-order rational difference equation such as $${ x_{n+1} = \frac{a+m\,x_n }{b+x_n } }$$
So, for your case, let $a=\frac AD$, $m=\frac BD$ and $b=\frac CD$