Question: Suppose that ak I 0 as k . Prove that k=1 ak sin kx converges uniformly on any closed interval [a, b]

Suppose that ak ↓ I 0 as k → ∞. Prove that ∑∞k=1 ak sin kx converges uniformly on any closed interval [a, b] ⊂ (0, 2π).

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