TAOCP 1.2.7 Exercise 1

By definition, H_n = \sum_{k=1}^{n}\frac1k.

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Section 1.2.7: Harmonic Numbers

Exercise 1. [01] What are $H_0$, $H_1$, and $H_2$?

Verified: no
Solve time: -

By definition,

$$ H_n = \sum_{k=1}^{n}\frac1k. $$

The empty sum gives

$$ H_0 = 0. $$

Furthermore,

$$ H_1 = 1, \qquad H_2 = 1+\frac12 = \frac32. $$

Therefore,

$$ \boxed{H_0=0,\quad H_1=1,\quad H_2=\frac32.} $$