Consider $s_n=\{2,1,\frac{4}{5},\frac{5}{7},\frac{2}{3}, \ldots\}$
What are some techniques and tips that I can use to find the rules for such series? I find is extremely hard to do so and would like some help.
EDIT: I'm not necessarily, looking for the rule of the specific example given, but some guidelines on to find rules on my own.
To me, it seems that it can be written into $$\left\{\frac{n+1}{2n-1}: n\geq1\right\}.$$