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Equation 9 · Part 12 · How Claude Code's Memory Actually Persists Across Sessions

Ending index or upper bound: n

Costn=1.25 c Tp+(n−1) (0.1 c Tp)+c∑i=1nTv,i\mathrm{Cost}_n = 1.25\,c\,T_p + (n-1)\,(0.1\,c\,T_p) + c\sum_{i=1}^{n} T_{v,i}
nn

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

n appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

…a documented 1.25 times the base price of an input token; a cache read, on every subsequent turn that reuses it, costs a documented one-tenth of that base price [ 5 ] . For a stable prefix of TpT_p tokens reused across n turns of a session, against a per-token base price c , the total cost of that prefix is Costn=1.25 c Tp+(n−1) (0.1 c Tp)+c∑i=1nTv,i\mathrm{Cost}_n = 1.25\,c\,T_p + (n-1)\,(0.1\,c\,T_p) + c\sum_{i=1}^{n} T_{v,i}. where the final sum covers each turn’s own variable content. Past the first turn, every further read of the same CLAUDE.md content costs a tenth of an uncached read — caching is…

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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.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.