Thread: 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

limit L or limit L + K ?

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 .

The sequence converges to L means that, given any there exist an integer N such that if n> N, . For the sequence just shift N to N+k