# Algebra of limits property proof

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• February 5th 2013, 03:58 PM
sakuraxkisu
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 :)
• February 5th 2013, 04:04 PM
jakncoke
Re: Algebra of limits property proof
limit L or limit L + K ?
• February 5th 2013, 04:14 PM
Plato
Re: Algebra of limits property proof
Quote:

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 $(s_{n+k})$.
• February 5th 2013, 06:03 PM
HallsofIvy
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