Originally Posted by

**ah-bee** Prove that if the sequence a(n+k) converges to l then the sequence a(n) also converges to l.

My proof basically looks like this:

there exists N s.t. n+k>n>N.

Assume the sequence a(n+k) converges to l and that the sequence a(n) diverges. By the definition: there exists L>0 s.t. for every K>0, there exists N that is an integer s.t n which is also an integer n>N -> |a(n+k)-L|<K

This means that if the sequence a(n) converges, then the sequence a(n+k) also converges because n+k>n>N.