BetterMath Blog
Blog
Articles, puzzles, classroom practice and activities: the mathematics behind the course, and how to study and teach it.
Articles
Antidifferentiation and integration are the same thingWhat is the opposite of a derivative, and why does it find areas?5 October 2026
·5 min readProofs in MathematicsHow can two facts prove infinitely many statements?3 October 2026
·11 min readAdding infinitely many numbersHow can a sum that never ends have a finite answer?29 September 2026
·1 min readWhy area and slope are the same calculationWhy does undoing a derivative give you an area?29 September 2026
·4 min readHow to study with BetterMathWhy are the notes so long?28 September 2026
·2 min read
·5 min readProofs in MathematicsHow can two facts prove infinitely many statements?3 October 2026
·11 min readAdding infinitely many numbersHow can a sum that never ends have a finite answer?29 September 2026
·1 min readWhy area and slope are the same calculationWhy does undoing a derivative give you an area?29 September 2026
·4 min readHow to study with BetterMathWhy are the notes so long?28 September 2026
·2 min read
Try this
Add a half, then a quarter, then an eighth, and keep going.
½ + ¼ + ⅛ + …
- Sum so far
- 63/64 = 0.984375
- Gap still left
- 1/64 = 0.015625
Each new term fills exactly half of the gap that is left, so the gap halves but never closes. Add them all, and the sum is exactly 1.
Read why the sum is exactly 1 >The triangle on the cover
Pascal's triangle: each number is the sum of the two above it.
Select any number.
The binomial theorem, Chapter 2 >