# limit-preserving

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##### 1: 3.9 Acceleration of Convergence

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►A transformation of a convergent sequence $\{{s}_{n}\}$ with limit
$\sigma $ into a sequence $\{{t}_{n}\}$ is called

*limit-preserving*if $\{{t}_{n}\}$ converges to the same limit $\sigma $. ►The transformation is*accelerating*if it is limit-preserving and if … ►It may even fail altogether by not being limit-preserving. …