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|Σ∞i=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}.