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What is the best way to prove a series is convergent or divergent?
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You are going to think I am joking. I am not. The best way is the way you can think of and understand that actually proves it so. All methods exist for a reason. They were useful. Do not think you can just discard one or two methods because they are useless. It just is not the case. Learn them all. Use them all. Care about them all. They will all be your friends.
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