The shift rule is a mathematical rule for
sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is calle ...
s and
series
Series may refer to:
People with the name
* Caroline Series (born 1951), English mathematician, daughter of George Series
* George Series (1920–1995), English physicist
Arts, entertainment, and media
Music
* Series, the ordered sets used in ...
.
Here
and
are
natural numbers.
For sequences, the rule states that if
is a sequence, then it
converge
Converge may refer to:
* Converge (band), American hardcore punk band
* Converge (Baptist denomination), American national evangelical Baptist body
* Limit (mathematics)
* Converge ICT, internet service provider in the Philippines
*CONVERGE CFD s ...
s if and only if
also converges, and in this case both sequences always converge to the same number.
For series, the rule states that the series
converges to a number if and only if
converges.
[.]
References
{{DEFAULTSORT:Shift Rule
Sequences and series