I have the following 3-adic series fraction : $$\frac{((2\cdot3^8 + 3^9 + \mathcal{O}(3^{10})) k^7 + (2\cdot 3^6 + 3^7 + \mathcal{O}(3^8)) k^6 + \mathcal{O}(3^7)\cdot k^5 + \mathcal{O}(3^{10})\cdot k^3 + \mathcal{O}(3^8)\cdot k^2)} { ((2\cdot 3^4 + 2\cdot 3^5 + 3^6 + 3^7 + \mathcal{O}(3^9))\cdot k^8 + (1 + 2\cdot 3^2 + 3^4 + \mathcal{O}(3^6))\cdot k^6)}$$
Is there a way I can write it down as a single series?
I am only interested with the first few terms of the series. Also, I am using PARI and SAGE, is there a way I can do this using these softwares?
Your fraction seems to be of the form $$ \frac{ak^2+bk^3+ck^5+dk^6+ek^7}{Ak^6+Bk^8}=\frac{a+bk+ck^3+dk^4+ek^5}{A+Bk^2}k^{-4}\,. $$ I suggest that you calculate by hand as many as you need of the first few terms in the above formulation, and then make your substitutions for $a$, etc.