Methods to identify if the sequence converges or diverges

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Given a question asking us to decide whether a sequence divergences or convergences, I usually will first try to see if I can “let the sequence $a_n = f(x)$”, then I can use l’h Rule or just basic algebra to solve the limit (n to infinity) of $f(x)$ question then that’s also the limit for the sequence. If the first try failed I will try squeeze theorem. Is there any way to tell which method should I use before I start to calculate the limit? What kind of questions are mostly solved by either method?