Glossary

Terms used across the blog, with short definitions, links to the posts that introduce them, and lists of every post that uses each one. Hover any glossary term elsewhere on the site to see its definition without leaving the page.

convergence

The property of an infinite process — a sum, a sequence, an iteration — that it eventually settles arbitrarily close to a fixed value, called its limit. The opposite is divergence: the process either grows without bound or oscillates without ever picking a target.

Introduced in: What "Converges" Actually Means Used in: Why the Geometric Series Adds Up; A Note on What This Blog Is

geometric series (also: GP)

An infinite sum where each term is a fixed multiple of the previous one, written $a{\Sigma }_{r=0}^{\infty }{r}^n$. When $|r|<1$ the terms shrink fast enough that the whole sum settles on a finite value.

Introduced in: Why the Geometric Series Adds Up Used in: Why the Geometric Series Adds Up

limit

The value an infinite process approaches but typically never reaches. Saying a sequence has limit $L$ means: for any tolerance, no matter how small, the sequence eventually gets within that tolerance of $L$ and stays there.

Used in: Why the Geometric Series Adds Up; A Note on What This Blog Is

partial sum

The sum of just the first $n$ terms of an infinite series. Studying partial sums is how you make sense of an infinite sum: instead of trying to add infinitely many things at once, you watch where the partial sums go as $n$ grows.

Introduced in: Why the Geometric Series Adds Up Used in: What "Converges" Actually Means; Why the Geometric Series Adds Up