Let (a_n) be a convergent sequence with limit L and let k be a natural number. Show that (a_n+k) is also convergent with limit L.
Any help would be greatly appreciated
The sequence converges to L means that, given any $\displaystyle \epsilon> 0$ there exist an integer N such that if n> N, $\displaystyle |a_n- L|< \epsilon$. For the sequence $\displaystyle a_{n+k}$ just shift N to N+k