HSC questions are never designed to ask students to call upon concepts outside the syllabus. If you carefully look at the power series questions asked in the past, you don't need to know anything about power series to actually answer the question. Even though the context of the question may appear unfamiliar, the tools you have from the syllabus are sufficient to answer it.i am sorry for not being able to ask a clear cut question.
Have used mod arithmetic for many problems, i love doing olympiad questions in my free time. There are many tools that I can just quote and use. But in HSC its a different ball game.
They have asked power series in the past. If you have a vague understanding you will definitly get the question out. I am scared they are gonna chuck something like mod arith soon. Derrangements were even asked once.