What function correspond to this series expansion?

Thread starter QMrocks
Start date Dec 1, 2005
Tags

Expansion Function Series Series expansion

In summary, a series expansion is a mathematical technique used to represent a function as a sum of infinitely many terms. It is often used to approximate a function that is difficult to evaluate directly. It allows us to approximate a function with a simpler, more manageable expression, which can be useful in solving complex problems or analyzing the behavior of a function. Series expansions are typically calculated using mathematical formulas such as the Taylor or Maclaurin series, which involve taking derivatives and evaluating the function at a specific point and its derivatives. The purpose of finding the function that corresponds to a series expansion is to obtain a more accurate representation of the original function, which can be useful in analyzing its behavior and making predictions. The accuracy of a series expansion can be determined

Dec 1, 2005

QMrocks

Anyone knows what function correspond to this series expansion?

[tex]
\begin{align}
f(x)=1+x+x^2+x^3+...
\end{align}
[/tex]

Last edited: Dec 1, 2005

Physics news on Phys.org

Dec 1, 2005

shmoe

Science Advisor

Homework Helper

Look up geometric series

1. What is a series expansion?

A series expansion is a mathematical technique used to represent a function as a sum of infinitely many terms. It is often used to approximate a function that is difficult to evaluate directly.

2. Why use a series expansion?

A series expansion allows us to approximate a function with a simpler, more manageable expression. This can be useful in solving complex problems or analyzing the behavior of a function.

3. How is a series expansion calculated?

A series expansion is typically calculated using a mathematical formula, such as the Taylor or Maclaurin series. These formulas involve taking derivatives of the function at a specific point and evaluating the function at that point and its derivatives.

4. What is the purpose of finding the function that corresponds to a series expansion?

The purpose of finding the function that corresponds to a series expansion is to obtain a more accurate representation of the original function. This can be useful in analyzing the behavior of the function and making predictions about its values at different points.

5. How do you determine the accuracy of a series expansion?

The accuracy of a series expansion can be determined by comparing its values to the values of the original function at different points. Generally, the more terms included in the series expansion, the more accurate it will be.