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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Pls create a another problem proposal just the example below. 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0f5758c-87ee-49d1-9544-6a578931d890%2Ff7ac12fb-6580-432b-909d-b5f485657672%2Fc5lij2n_processed.jpeg&w=3840&q=75)
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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