scholarly journals Approximating the Sum of Infinite Series of Non Negative Terms with reference to Integral Test

2020 ◽  
Vol 37 (1-2) ◽  
pp. 63-70
Author(s):  
Daya Ram Paudyal
Keyword(s):  
Infinite Series ◽  
Historical Background ◽  
Integral Test ◽  
Improper Integrals ◽  
The Given

This paper describes a method of obtaining approximate sum of infinite series of positive terms by using integrals under its historical background. It has shown the application of improper integrals to determine whether the given innate series is convergent or divergent. Here, the limits of the integrals and the series usually extend to infinity though they may be slowly convergent. We have also established a relation to approximate the sum of infinite series of positive terms with a suitable example.

A Simplified Integral Test for the Convergence of Infinite Series

1931 ◽  
Vol 38 (4) ◽  
pp. 205
Author(s):  
Raymond W. Brink
Keyword(s):  
Infinite Series ◽  
Integral Test

scholarly journals Relationship between Sumudu and Some Efficient Integral Transforms

2020 ◽  
Vol 9 (3) ◽  
pp. 153-159 ◽  
Keyword(s):  
Infinite Series ◽  
Initial Value Problems ◽  
Integral Transforms ◽  
Renewal Equation ◽  
Physical Explanation ◽  
Initial Value ◽  
Gamma Functions ◽  
Improper Integrals ◽  
The Relationship

Nowadays integral transforms are most appropriate techniques for finding the solution of typical problems because these techniques convert them into simpler problems. Finding the solution of initial value problems is the main use of integral transforms. However, there are so many other applications of integral transforms in different areas of mathematics and statistics such as in solving improper integrals of first kind, evaluating the sum of the infinite series, developing the relationship between Beta and Gamma functions, solving renewal equation etc. In this paper, scholars established the relationship between Sumudu and some efficient integral transforms. The application section of this paper has tabular representation of integral transforms of some regularly used functions to demonstrate the physical explanation of relationship between Sumudu and mention integral transforms.

scholarly journals Errors In Using Convergence Tests In Infinite Series

2020 ◽  
Vol 13 (2) ◽  
pp. 113-127
Author(s):  
Murat GENÇ ◽  
Mustafa AKINCI
Keyword(s):  
Undergraduate Students ◽  
Infinite Series ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Test Results ◽  
Convergence Criteria ◽  
Convergence Test ◽  
Comparison Test ◽  
The Given

Abstract: The present study aimed to identify the errors made by pre-service elementary mathematics teachers while investigating the convergence of infinite series. A qualitative exploratory case study design was used with a total of 43 undergraduate students. Data were obtained from a test administered in a paper-and-pencil form consisting of seven open-ended questions. The data analysis was done using descriptive and content analysis techniques. Findings were presented as follows: inappropriate test selections; failure to check convergence criteria; incorrect use of a comparison test; limit comparison test error; re-test convergence test results; considering ∑ as a multiplicative function; misunderstanding of special series; considering that series has no character when the convergence test is inconclusive; confusing sequences with series; misunderstanding of the nth-term test; misinterpretation of convergence test results. Findings showed that students with insufficient procedural knowledge had difficulty in solving the given problem even if they understood it, whereas those with insufficient conceptual knowledge could not literally understand what they did even if they solved the problem. Therefore, the establishment of a moderate balance between procedural and conceptual knowledge in the learning of the convergence of series is essential in reducing the errors or learning difficulties for developing deep mathematical understanding

An Alternative to the Integral Test for Infinite Series

1972 ◽  
Vol 79 (6) ◽  
pp. 634-635
Author(s):  
G. J. Porter
Keyword(s):  
Infinite Series ◽  
Integral Test

Added Moment of Inertia of Rolling Ship Sections

1982 ◽  
Vol 26 (02) ◽  
pp. 89-93
Author(s):  
P. P. Hsu ◽  
L. Landweber
Keyword(s):  
Free Surface ◽  
Infinite Series ◽  
Laurent Series ◽  
Low Frequency ◽  
Moment Of Inertia ◽  
Section Area ◽  
Family Of Curves ◽  
Section Rolling ◽  
The Given ◽  
Two Parameter

An expression for the added moment of inertia of a ship section rolling at low frequency at a free surface, in terms of the coefficients of the Laurent series of the function which maps the given section into a circle, has been derived. The method is applied to the two-parameter family of Lewis forms and the results are presented as a family of curves which gives the coefficient of the added moment of inertia as a function of the thickness ratio and the section-area coefficient of a form. A second application is to a square section, for which the Laurent expansion is an infinite series.

Numerical Methods I

2021 ◽  
Author(s):  
Boris Obsieger
Keyword(s):  
Numerical Methods ◽  
Direct Methods ◽  
Historical Background ◽  
Random Errors ◽  
Practical Application ◽  
Fourth Degree ◽  
Numerical Errors ◽  
The Third ◽  
Numeral Systems ◽  
The Given

Textbook, established at several universities. Second edition. *** Written primarily for students at technical studies. Valuable handbook for engineers, PhD students and scientists. *** Published in several variants. *** Seven chapters. In the first chapter, a historical background and basic properties of various numeral systems, as well as conversion of numbers from one system to another are briefly explained. In the second chapter, numbers in digital computers, namely integers and floating point numbers are described. This helps the reader to choose precision and range limits of stored numbers. The third chapter explains constant variables and related numerical errors, including error propagation and algorithm instability. The fourth and fifth chapters explain random variables and related random errors, uncertainty, confidence level, as well as propagation of random errors. Various types of regression analyses of experimental data are described in the sixth chapter. Direct methods for finding roots of the third and fourth degree polynomials are described in the seventh chapter, followed by general iterative methods for polynomials of any degree. *** Why the presented topics are so important? Simply, they are common to all numerical methods. *** Practical application is supported by 84 examples and 17 algorithms. For reasons of simplicity, algorithms are written in pseudo-code, so they can easily be implemented in any computer program. Finally, the given text with 98 figures and 52 tables represents a valuable background for understanding, applying and developing various numerical analyses.

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