Shift rule
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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_{n}) is a sequence, then it converges if and only if (a_{n+N}) also converges, and in this case both sequences always converge to the same number. For series, the rule states that the series \sum\limits_{n=1}^\infty a_{n} converges to a number if and only if \sum\limits_{n=1}^\infty a_{n+N} converges.
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_{n}) is a sequence, then it converges if and only if (a_{n+N}) also converges, and in this case both sequences always converge to the same number. For series, the rule states that the series \sum\limits_{n=1}^\infty a_{n} converges to a number if and only if \sum\limits_{n=1}^\infty a_{n+N} converges. ==References==
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