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

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

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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 a[n] –> L as n –> infinity, you need to show that you can make |a[n] – 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.

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