Equation 2 · Part 16 · Apprenticeship as Information Transfer

Ending index or upper bound: n

C_n = C_0 \prod_{k=1}^{n} f_k + \sum_{k=1}^{n} i_k \prod_{j=k+1}^{n} f_j

n

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 product. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionEnding index or upper bound: nArticle meaning

The passage around this formula

A useful way to make the retention condition inspectable is to write the accumulated complexity after n transmission steps as a product of per-step fidelities plus whatever is added along the way: $C_n = C_0 \prod_{k=1}^{n} f_k + \sum_{k=1}^{n} i_k \prod_{j=k+1}^{n} f_j$ . Here $C_0$ is the starting repertoire, $f_k$ is the fraction of it that survives step k , and $i_k$ is what is genuinely added at that step. This expression is illustrative rather than a…

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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 article section

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