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**[SOLVED] Limit n[1 - exp(ia/n)]**

**Homework Statement**

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?