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The shift rule is a mathematical rule for sequences and series.
Here n {\displaystyle n} and N {\displaystyle N} are natural numbers.
For sequences, the rule states that if {\displaystyle } is a sequence, then it converges if and only if {\displaystyle } also converges, and in this case both sequences always converge to the same number.
For series, the rule states that the series ∑ n = 1 ∞ a n {\displaystyle \sum \limits _{n=1}^{\infty }a_{n}} converges to a number if and only if ∑ n = 1 ∞ a n + N {\displaystyle \sum \limits _{n=1}^{\infty }a_{n+N}} converges.