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

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  • Shift rule (en)
  • 移位法则 (zh)
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  • 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. For series, the rule states that the series converges to a number if and only if converges. (en)
  • 移位法则 是关于序列和级数的一个数学法则。 以下讨论的 和 都是自然数。 对于序列,这条法则称,如果 是一个序列,那么它收敛当且仅当 收敛,并且此时这两个序列总是收敛到相同的值。 对于级数,这条法则称, 收敛到某个数,当且仅当 收敛。 (zh)
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  • 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. For series, the rule states that the series converges to a number if and only if converges. (en)
  • 移位法则 是关于序列和级数的一个数学法则。 以下讨论的 和 都是自然数。 对于序列,这条法则称,如果 是一个序列,那么它收敛当且仅当 收敛,并且此时这两个序列总是收敛到相同的值。 对于级数,这条法则称, 收敛到某个数,当且仅当 收敛。 (zh)
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