How do I turn an infinite series into a function in the form y=f(x)?

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I am trying to determine the area between the curves defined by $\sum^{n}_{k=1} \frac {1}{k}$ and $y=\ln n$, which don't intersect. How can I turn the series $\sum^{n}_{k=1} \frac {1}{k}$ into a function in the form $y=f(x)$ so I can apply the Newton-Coates formulae (the Trapezoidal rule)?