series_howto_relaxed.pdf - How to determine whether X an...

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How to determine whether X n =1 a n converges or diverges. Throughout, let f be a function satisfying f ( n ) = a n . Question 1: Can my series converge (i.e. does lim n →∞ a n exist and does lim n →∞ a n = 0?) If no : You’re done; n =1 a n di verges. If yes : Your series may converge. Go to Question 2 . Question 2: Does my series have negative terms? If no : You have a positive series. Go to Question 3 . If yes : Go to Question 5 . Question 3: Is my series a geometric series or a p -series? If yes : Use the info you know about geometric series and/or p -series and you’re done. If no : Go to Question 4 .
Question 4: If I squint at my series, does it kinda-sorta look like a geometric series or a p -series?

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