Equation 10 · Part 12 · The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol
Ending index or upper bound: k
What this part means
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
Its job in the formula
k occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Ending index or upper bound: k→Article meaning
The passage around this formula
Model it simply. Suppose a session runs for k turns, and each turn adds on average tokens of new tool result to a transcript that is resent in full on every request, because nothing is evicting or compressing it. The tokens billed on turn i include roughly i tokens of accumulated result history, so the total billed across the…
Learn the underlying idea
Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.
Open the illustrated sums and products: repeat an operation over an index guide →
See this notation across published equations →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.