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 :)

Printable View

- Feb 5th 2013, 02:58 PMsakuraxkisuAlgebra 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 :) - Feb 5th 2013, 03:04 PMjakncokeRe: Algebra of limits property proof
limit L or limit L + K ?

- Feb 5th 2013, 03:14 PMPlatoRe: Algebra of limits property proof
- Feb 5th 2013, 05:03 PMHallsofIvyRe: Algebra of limits property proof
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