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Why does the series not exist?

Why does the series not exist?-example-1
User Town
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Explanation:

(7n − 5) / (2n + 5) approaches 7/2 as n approaches infinity. However, this is an alternating series. So the function is fluctuating between -7/2 and +7/2. So the limit does not exist.

User Herpderp
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