Numerical Series and Series of Functions

Alessandro Fonda
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Alessandro Fonda: Università degli Studi di Trieste, Dipartimento di Matematica e Geoscienze

Chapter 8 in A Modern Introduction to Mathematical Analysis, 2023, pp 203-232 from Springer

Abstract: Abstract Let V be a normed vector space. Given a sequence (a k)k in V , the associated “series” is the sequence (s n)n defined by s 0 = a 0 , s 1 = a 0 + a 1 , s 2 = a 0 + a 1 + a 2 , … s n = a 0 + a 1 + a 2 + ⋯ + a n , … $$\displaystyle \begin {array}{lll} &&s_0=a_0\,,\\ &&s_1=a_0+a_1\,,\\ &&s_2=a_0+a_1+a_2\,,\\ &&\; \dots \\ &&s_n=a_0+a_1+a_2+\dots +a_n\,,\\ &&\; \dots \end {array} $$

Date: 2023
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DOI: 10.1007/978-3-031-23713-3_8

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