Limits

Calculus Level 4

Let \(S_n = \sin(x) + \sin(2x) + \sin (3x) + \cdots + \sin(nx) \). Find the following limit:

\[\large \lim_{n \to \infty} \frac{S_1 + S_2 + S_3 + \cdots + S_n}n \]

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