# Thread: Algebra of limits property proof

1. ## Algebra of limits property proof

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

2. ## Re: Algebra of limits property proof

limit L or limit L + K ?

3. ## Re: Algebra of limits property proof

Originally Posted by sakuraxkisu
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.
I am sure that he/she means $(s_{n+k})$.

4. ## Re: Algebra of limits property proof

The sequence converges to L means that, given any $\epsilon> 0$ there exist an integer N such that if n> N, $|a_n- L|< \epsilon$. For the sequence $a_{n+k}$ just shift N to N+k