Which of the following is **false**?

**A:** \(\quad \displaystyle \sum_{n=1}^{\infty} \sin\dfrac{1}{n}\) diverges.

**B:** \(\quad \displaystyle \sum_{n=1}^{\infty} \sin\dfrac{1}{n^2}\) converges.

**C:** \(\quad \displaystyle \sum_{n=1}^{\infty} \cos\dfrac{1}{n}\) diverges.

**D:** \(\quad \displaystyle \sum_{n=1}^{\infty} \cos\dfrac{1}{n^2}\) converges.

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