Equation 25 · Part 15 · The Economics and Physical Limits of Running AI Agents at Scale
Numerator: n(n-1)
What this part means
The complete quantity above the fraction bar.
Its job in the formula
n(n-1) occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Numerator: n(n-1)→Article meaning
The passage around this formula
Prompt caching is the documented fix for exactly this, and it is worth being precise about what it fixes and what it does not. Anthropic’s automatic caching, recommended for multi-turn use, places a single cache marker at the end of a request; the system caches everything up to that marker, and the next request’s identical prefix is read from cache rather than reprocessed [ 2 ] . Anthropic’s documentation walks through exactly this pattern for a growing conversation: at each new turn, the system prompt and all prior turns are read from cache, and only the newest exchange is freshly written to cache for next time [ 2 ] . A cache read costs a tenth of the base input price; a five-minute cache…
Learn the underlying idea
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.