### Prove that W is a Subspace of V

Let F be the field of real numbers and let V be the set of all sequences: (a_1, a_2, ..., a_n, ...), a_i belongs to F, where equality, addition and scalar multiplication are defined component wise. Then V is a vector space over F. Let W = {(a_1, a_2, ..., a_n, ...) belongs to V | lim n -> infinity a_n = 0}. Prove t