# A trigonometric inequality

Algebra Level 5

Find the smallest integer $$N$$ such that for all positive integers $$n$$ $\lvert \sin \frac{1}{100}+\sin \frac{2}{100}+...+\sin \frac{n}{100} \rvert <N$

Details and assumptions

You may use the fact that $$\pi$$ is an irrational number.

Clarification: The measurements are done in radians, not degrees.

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