Prove that u is a subspace of v and is contained in w

Question

Problem:

Prove that U is a Subspace of V and is Contained in W

What is presented below has many missing parts as the full question could not be copied properly.

Let F be the field of real numbers and let V be the set of all sequences:

( a₁,a₂,...,a_n,...), a_i∈F, where equality, addition and scalar multiplication are defined component wise. Then V is a vector space over F.

Let W = {( a₁, a₂,...,a_n,...)∈V|limn_→∞ a_n = 0}.Then W is a subspace of V.

Let U = {( a₁, a₂,...,a_n,...)∈V|Σ^∞_i=1 a²_iis finite}

Prove that U is a subspace of V and is contained in W,

where W = {( a₁,a₂,...,a_n,...)∈V|limn_→∞ a_n = 0}.