Complex number 2!

Calculus Level 4

For an integer \(p\), define \[f_p(\alpha) = e^{i\alpha /p^2} . e^{2i\alpha /p^2} . e^{3i\alpha /p^2} ........ e^{pi\alpha /p^2}\]

Evaluate\(\displaystyle \lim_{n \to \infty} f_n(\pi)\).

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