Solved cryptogram
Add a half, then a third, then a quarter, and the running total passes any number you name.
Mathematics Facts, sourced to Wolfram MathWorld.
Solve it yourself
This fact is a cryptogram here: 70 letters over 19 different ones, graded medium.
Or go to the puzzle’s own page first.
What it means
The terms shrink toward nothing and the sum still grows without limit, which is why the series is worth knowing. Group the terms as one half, then two terms near a quarter, then four near an eighth, and each group is worth at least a half. There are unlimited groups, so the total is unlimited. It grows agonizingly slowly, though: reaching a hundred takes more terms than there are atoms in a person.
The claim comes from Wolfram MathWorld.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultymedium
- Length70 letters, 19 of them different
Nearby in the collection
The facts either side of this one.
- Wolfram MathWorldmedium, 72 letters
- Wolfram MathWorldhard, 66 letters
- Wolfram MathWorldhard, 72 letters
- Wolfram MathWorldhard, 68 letters
About as hard as this one
Scored closest to it by the model behind our guide to solving cryptograms.
- Wolfram MathWorldmedium, 79 letters
- MacTutor History of Mathematicsmedium, 77 letters
- Wolfram MathWorldmedium, 80 letters
- MacTutor History of Mathematicsmedium, 72 letters