Let {$\displaystyle {a_n}$} be a sequence and k be a positive integer.

a) If {$\displaystyle {a_n}$} converges to L, what are the limits of {$\displaystyle {a_{99+n}}$} and {$\displaystyle {a_{k+n}}$}? Why?

b) If {$\displaystyle {a_n}$} diverges, what is the limit of {$\displaystyle {a_{k+n}}$}? Why?