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# Exact value seems to be hard!

Is there any way to find the exact value of $$A_n = 1 + \frac{1}{2} + \frac{1}{3} +...+ \frac{1}{n}$$? And is there a closed form?

Note by Steven Jim
5 months, 2 weeks ago

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This is called the Harmonic series, and there is no closed form. However, the sum $$1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}$$ is approximately $$\log n$$. See the following for more details.

https://en.wikipedia.org/wiki/Harmonicseries(mathematics)

- 5 months, 2 weeks ago

Thanks! Very much appreciated!

- 5 months, 2 weeks ago