I need help proving this question:
Suppose lim(n->oo) An = L and let Bn = A2n for all n being Natural numbers. Prove that lim(n->oo) Bn = L
More generally, if a sequence converges to L, then every subsequence also converges to L. I personally would be inclined to use a direct proof rather than proof by contradiction. Since converges to L, given any , there exist N such that if n> N, then . Since , take n> 2N.
(If you do use proof by contradiction, note that you cannot assume that converges. That is, may not exist.)