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Proving That the Series sin(1/n) Diverges — Full Explanation
In this video, we prove that the infinite series sum_{n=1}^{infty} sinleft(frac{1}{n} ight) is divergent. Using the limit comparison test with the harmonic series, we show that sinleft(frac{1}{n} ight) sim frac{1}{n} as n to infty. Since the harmonic series sum frac{1}{n} diverges, the series sum sin(1/n) must also diverge. This proof is simple ...
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