Sequences and series

Topics

Fourier series

Add sines and cosines to approximate a periodic function, and change the number of terms N to watch convergence and the Gibbs phenomenon.

Interactive

Analysis High-school concept

One rule for the next term can make a partial sum converge or diverge, or send an orbit into a dense cloud of points.

Works

Work

Arithmetic and geometric sequences

Functions and analysis High-school concept

Bars and equal-height rectangles show arithmetic and geometric sequences and the formulas for their sums.

Work

Fibonacci spiral

Geometry Intuitive exploration

Quarter-circles on squares of Fibonacci side lengths approximate a logarithmic spiral.

Work

Basel problem

Functions and analysis University concept

Partial sums, stacked areas, and a sine product picture the sum of reciprocal squares, equal to pi squared over 6.

Exam visualizations

Exam

A lottery wait and the geometric distribution

113 AST Mathematics I, Multiple select 4 Geometric distributionExpected value

113 AST Mathematics I, Multiple select 4: the geometric distribution, counted as trials until the first win, gives the mean wait, the chance from finitely many tokens, and the nine-tenths cutoff.

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