Hi!! I'm a 2nd year CS Major. Excited to meet yall!! My hobbies include basketball, tennis, table tennis, chess, and YouTube.

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Questions: 

1. Is there a more systematic way of finding subsequential limits? For some of the homework problems, I just sort of guessed some subsequences and their limits and it was easy to tell, but I'd imagine its hard to do that for other sequences.

2. I'm a bit confused about the proof to show that cauchy implies convergence. How do we know what epsilon to choose so that we get a contradiction (here we chose (A-B)/3)

3. In lecture, we went over a lemma that limsup a_n = A then for all epsilon > 0, N > 0, there exists n > N such that |a_n - A| < epsilon, but isn't that true by definition. Why did we have to do a more formal proof of it?

4. I see the common approach in 104 problems as to take cases when something is finite or infinite. This can help a lot, but is there a general sort of problem where I can use this strategy? A lot of times I get stuck and don't know what to use.

5. Is there a specific strategy for dealing with logarithms. None of the series tests seem friendly to this function. Is it always like some clever comparison?