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index of summation

The counter variable in Σ notation, and the start/stop values that bound it.

In $\sum_{k=1}^{n} a_k$ , $k$ is the index of summation — a dummy variable that can be renamed freely without changing the sum — while $1$ is the lower limit and $n$ is the upper limit. Summation is linear: constants factor out and separate sums can be split apart or recombined term by term.

See also

series

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