Shift rule

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

For sequences it states, if $(a n)$ is a sequences and converges to a number if and only if $(a n + N)$ also converges to the same number too.

For series it states, if the series ${\Sigma^{\infty}_{n=1}}(a_{n})$ converges to a number if and only if ${\Sigma^{\infty}_{n=1}}(a_{n+N})$ converges to the same number too.