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n=1 Let {an be a sequence of real numbers. Then, Σan is absolutely con- verge if and only if an converge [1]. The Cauchy Convergence Criterion imply that every absolutely convergence series are convergence [2]. The goal of this study is to generalized the notion of absolute convergence by replacing the absolute value || by a nonnegative function f. Let f: R→ [0, +∞) be a function. We say that an is f-converge if and only if f(an) converge. The goal of this study is to give a test that determine when the series is f-converge, similar to root test [3] and ratio test [4] in absolutely converge.

n=1 Let {an be a sequence of real numbers. Then, Σan is absolutely con- verge if and only if an converge [1]. The Cauchy Convergence Criterion imply that every absolutely convergence series are convergence [2]. The goal of this study is to generalized the notion of absolute convergence by replacing the absolute value || by a nonnegative function f. Let f: R→ [0, +∞) be a function. We say that an is f-converge if and only if f(an) converge. The goal of this study is to give a test that determine when the series is f-converge, similar to root test [3] and ratio test [4] in absolutely converge.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi, gave me another set of problem that is related to the problems on the picture. Or any great problem proposal that is about real analysis, calculus, topology, or abstract algebra. Thank you.

=1 Let {an be a sequence of real numbers. Then, an is absolutely con- verge if and only if Σan converge [1]. The Cauchy Convergence Criterion imply that every absolutely convergence series are convergence [2]. The goal of this study is to generalized the notion of absolute convergence by replacing the absolute value | | by a nonnegative function f. an is f-converge if Let f R [0, +∞) be a function. We say that and only if f(an) converge. The goal of this study is to give a test that determine when the series is f-converge, similar to root test [3] and ratio test [4] in absolutely converge.
Transcribed Image Text:=1 Let {an be a sequence of real numbers. Then, an is absolutely con- verge if and only if Σan converge [1]. The Cauchy Convergence Criterion imply that every absolutely convergence series are convergence [2]. The goal of this study is to generalized the notion of absolute convergence by replacing the absolute value | | by a nonnegative function f. an is f-converge if Let f R [0, +∞) be a function. We say that and only if f(an) converge. The goal of this study is to give a test that determine when the series is f-converge, similar to root test [3] and ratio test [4] in absolutely converge.
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