Let \( I_{n}=\int_{0}^{\pi} \frac{\sin ^{2}(n x)}{\sin ^{2} x} d x,...

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Let \( I_{n}=\int_{0}^{\pi} \frac{\sin ^{2}(n x)}{\sin ^{2} x} d x, n \in N \),
\( \mathrm{P} \)
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(1) \( I_{n+2}+I_{n}=2 I_{n+1} \)
(2) \( I_{n}=I_{n+1} \)
(3) \( I_{n}=\mathrm{n} \pi \)
(4) \( I_{1}, I_{2}, I_{3}, \ldots . I_{n} \) are harmonic progression
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