Let (x) = a 1 sin x + a 2 sin 2x + ...+ a n sin
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Let ƒ(x) = a1 sin x + a2 sin 2x + ...+ an sin nx, where a1, a2,..., an are real numbers and where n is a positive integer. Given that |ƒ(x)| ≤ sin x| for all real x, prove that |a1 + 2a2 + · · · + nan| ≤ 1.
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