Shift rule

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

Here $n$ and $N$ are natural numbers.

For sequences, the rule states that if $(a_)$ is a sequence, then it converges if and only if $(a_)$ also converges, and in this case both sequences always converge to the same number.

For series, the rule states that the series $\sum\limits_^\infty a_$ converges to a number if and only if $\sum\limits_^\infty a_$ converges..

References

{{DEFAULTSORT:Shift Rule
Sequences and series