MHB Can a Numerical Series Converge to a Functional Series?

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The discussion revolves around the relationship between numerical convergent series and functional series. A participant questions whether a numerical convergent series can also be a convergent functional series, noting their understanding that the reverse is true. Clarification is sought on the definitions of numerical and functional series, specifically asking if a numerical series consists of numerical values for each term. The conversation highlights the need for precise definitions to explore the convergence properties of these series. Understanding these concepts is essential for further analysis of their interrelation.
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hi everyone ! i have a question ,

Can a numerical convergent series be a convergent functional series?

I know only the other way that a convergent functional series can be a convergent numerical series because i take a function as a constant so i have a numerical series and it converges.
 
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andijaupi said:
hi everyone ! i have a question ,

Can a numerical convergent series be a convergent functional series?

I know only the other way that a convergent functional series can be a convergent numerical series because i take a function as a constant so i have a numerical series and it converges.

Hi andijaupi, :)

Could you please tell me what you meant by a numerical series (is it something that has numerical values for each term? Example, $\sum_{i=0}^\infty 1/i^2$) and a functional series?
 
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