Representing a Sum of a Series as a Function

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In summary, a series in mathematics is a sum of numbers that follows a specific pattern, while a function is a mathematical rule or relationship between two variables. A series can be represented as a function by finding a rule or formula that relates the terms of the series to their corresponding position in the series. The difference between a finite and infinite series is that a finite series has a limited number of terms while an infinite series has an infinite number of terms. Examples of series that can be represented as functions include geometric series, arithmetic series, and power series. These series have specific formulas that relate the terms to their position in the series, allowing them to be represented as functions.
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Homework Statement

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Find a function to represent the series and then find f(?) that will represent its sum.

The Attempt at a Solution

I kind of understand how to come up with a function, but then how do I know what value to plug into the function to get the sum? Thank you for any help!

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it should help to know that $$\tan{x}=\sum_{n=0}^{\infty}(-1)^{n}\frac{x^{2n+1}}{2n+1}$$

What is a series in mathematics?

A series in mathematics is a sum of numbers that follows a specific pattern. It is an infinite sequence of terms that are added together to form a sum.

What is a function?

A function is a mathematical rule or relationship between two variables. It takes an input value and produces a corresponding output value.

How can a series be represented as a function?

A series can be represented as a function by finding a rule or formula that relates the terms of the series to their corresponding position in the series. This function can then be used to calculate the sum of the series for any given number of terms.

What is the difference between a finite and infinite series?

A finite series has a limited number of terms, while an infinite series has an infinite number of terms. In other words, a finite series has a specific end point, while an infinite series continues on forever.

What are some examples of series that can be represented as functions?

Some examples of series that can be represented as functions include geometric series, arithmetic series, and power series. These series have specific formulas that relate the terms to their position in the series, allowing them to be represented as functions.

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