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The problem statement, all variables and given/known data

What is the limit of n[1 - exp(ia/n)] as n goes to infinity (a is fixed real number).

The attempt at a solution

n[1 - exp(ia/n)] = n / [1 - exp(ia/n)]^{-1}and by using l'Hosptal's rule, I get that the limit diverges. Now how can I do this without relying on l'Hospital's rule?

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# Homework Help: Limit n[1 - exp(ia/n)]

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