Exercise 1.3.21

Question

Let $\mathrm{V}$ denote the vector space of sequences in $R$, as defined in Example 5 of Section 1.2. Show that the set of convergent sequences $\left(a_{n}\right)$ (that is, those for which $\lim _{n \rightarrow \infty} a_{n}$ exists) is a subspace of V.

Jephian C.-H. Lin · Accepted Answer

In calculus course it will be proven that $\{a_n+b_n\}$ and $\{ca_n\}$ will converge. And zero sequence, that is sequence with all entris zero, will be the zero vector.

Exercise 1.3.21

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Exercise 1.3.21

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