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


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,...,an,...), ai∈F, where equality, addition and scalar multiplication are defined component wise. Then V is a vector space over F.

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

Let U = {( a1, a2,...,an,...)∈V|Σi=1 a2iis finite}

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

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

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