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Question Number 166616 by qaz last updated on 23/Feb/22

calculate::lim_(n→∞) ((∣cos 1^2 ∣+cos ∣2^2 ∣+∣cos 3^2 ∣+...+∣cos n^2 ∣)/n)=(2/π)

$$\mathrm{calculate}::\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mid\mathrm{cos}\:\mathrm{1}^{\mathrm{2}} \mid+\mathrm{cos}\:\mid\mathrm{2}^{\mathrm{2}} \mid+\mid\mathrm{cos}\:\mathrm{3}^{\mathrm{2}} \mid+...+\mid\mathrm{cos}\:\mathrm{n}^{\mathrm{2}} \mid}{\mathrm{n}}=\frac{\mathrm{2}}{\pi} \\ $$

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