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Shift rule

From Wikipedia, the free encyclopedia

The shift rule is a mathematical rule for sequences and series.

Here and are natural numbers.

For sequences, the rule states that if is a sequence, then it converges if and only if also converges, and in this case both sequences always converge to the same number.[1]

For series, the rule states that the series converges to a number if and only if converges.[2]

References

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  1. ^ Ueltschi, Daniel (2011), Analysis –MA131 (PDF), University of Warwick, p. 31.
  2. ^ Alcock, Lara (2014), How to Think About Analysis, Oxford University Press, p. 102, ISBN 9780191035371.