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 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 Σ n = 1 ∞ ( a n ) converges to a number if and only if Σ n = 1 ∞ ( a n + N ) converges.