Kaylee's Annoying Problem

Level pending

After another entertaining class of Pre-Calculus, Kaylee decides to ask Sanjoy a question about Harmonic Sequences. Knowing he absolutely hates Sequences and Series, she finds this to be the opportune time to annoy him. She asks him: "In the harmonic sequence, 6, 3, 2, 3/2 ,…,what is the 10,000th term? Round your answer to the nearest thousandth place."

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