# The Loga-rhythm of Harmony

**Calculus**Level 5

\[\large \lim_{n \rightarrow \infty} \left[ f(H_{10^{n}}) \right]^{-\frac{1}{10^{n}}}\]

Let \(f\) be the Thomae function and \(H_{n}\) be the nth harmonic number. Evaluate the limit above.

\[\large \lim_{n \rightarrow \infty} \left[ f(H_{10^{n}}) \right]^{-\frac{1}{10^{n}}}\]

Let \(f\) be the Thomae function and \(H_{n}\) be the nth harmonic number. Evaluate the limit above.

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