Question: Evaluate lim _ { n to infty } left ( frac { i } { n } sum _

Evaluate
\lim _{n\to \infty }\left(\frac{i}{n}\sum _{i=1}^n\:cos\left(\frac{4k\pi }{9n}\right)\right) as a definite integral from 0 to 4pi /9

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