3.1 Sums & Products | 3.1 Sums & Products | Unit 3: Counting | Mathematics for Computer Science | Electrical Engineering and Computer Science

<Book Stacking: Video
3.1.1Arithmetic Sums: Video
3.1.2Perturbation by Young Gauss
3.1.3Geometric Sums: Video
3.1.4Annuities
3.1.5Book Stacking: Video
3.1.6Harmonic Numbers
3.1.7Integral Method: Video
3.1.8Integral Method Demystified
3.1.9Stirling's Formula: Video
3.1.10Applying Stirling's Formula
3.1.11Convergence of Geometric Series
3.1.12Summation
3.1.13Sum's Upper Lower Bounds
>Integral Method: Video

Harmonic Numbers

Which of the following are true?

Each Harmonic number is defined in terms of a simple summation.

\(H_n ::= \sum \limits_{i=0}^n \frac{1}{i} \).

The overhang of a stable stack of \(n \) books on the edge of a table is equal to the \(n \)-th Harmonic number.

In calculating the \(\bigtriangleup \)-overhang for the \((n+1) \)-th book that ensures stable stacking, the expression \(\bigtriangleup = \frac{\frac{1}{2}}{n+1} \) comes from the equality \(n \cdot \bigtriangleup = 1 \cdot (\frac{1}{2} - \bigtriangleup) \).

\(H_n ::= \sum \limits_{i=1}^n \frac{1}{i} \). The overhang of a stable stack of \(n \) books on the edge of a table is equal to half the \(n \)-th Harmonic number.