SEQUENCE CONVERGENCE How can we prove mathematically that a sequence is convergent or divergent?

One way is to breaak the proof up into steps, with each step justified by citing a theorem from the textbook. I illustrated this method at Example1. A more direct method: If you want to show that an --> L as n --> infinity, you need to show that you can make |an - L| as small as you want by choosing n sufficiently large.

So, for example, to start the proof that 1-(1/n) -->1, you need to think about how large you would need to make n in order to make | 1-(1/n) - 1| "small," arbitrarily small that is. More.

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