Equation 31 · Part 7 · The Economics and Physical Limits of Running AI Agents at Scale
Starting index or lower bound: i
What this part means
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Its job in the formula
i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Full expression→Starting index or lower bound: i→Article meaning
The passage around this formula
Holding = q constant across the trajectory — a simplification, since real failure rates are neither constant nor independent — the expected extra cost from retries is , and because increases with i , that extra cost is weighted toward the trajectory’s most expensive, latest steps rather than distributed evenly across it. A one-percent per-step retry rate is a rounding error at step five. Applied at step two hundred of an uncached or lightly cached loop, it is a rounding error on a much larger number.
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 article section
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