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Let {an be a sequence of real numbers. Then, an 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 fR [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.

Let {an be a sequence of real numbers. Then, an 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 fR [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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=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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