# Shift rule

For sequences it states, if ${\displaystyle (a_{n})}$ is a sequences then it converges if and only if ${\displaystyle (a_{n+N})}$ also converges, and in this case both sequences always converge to the same number.[1]
For series it states, the series ${\displaystyle {\Sigma _{n=1}^{\infty }}(a_{n})}$ converges to a number if and only if ${\displaystyle {\Sigma _{n=1}^{\infty }}(a_{n+N})}$ converges.[2]