# What is the sum of the series s(x) = 1 + cos(x) + (cos 2x)/2! + (cos 3x)/3! ...?

• thanksie037
In summary, a series is a set of numbers, terms, or expressions that are added together in a specific order. To find the sum of a series, you need to add all the terms in the series together, which can be done using a formula or by adding the terms manually. The formula for finding the sum of a series is S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term in the series. There are two types of series: arithmetic, where each term is obtained by adding a constant number to the previous term, and geometric, where each term is obtained by multiplying the previous term by a constant number
thanksie037

## Homework Statement

Find the sum of the series s(x) = 1 +cos(x)+ (cos2x)/2!+(cos3x)/3!...

## The Attempt at a Solution

i'm miserable at series. help?

thanksie037 said:
Find the sum of the series s(x) = 1 +cos(x)+ (cos2x)/2!+(cos3x)/3!...

## Homework Equations

Hi thanksie037!

Hint: this is the real part of what complex series?

## 1. What is a series?

A series is a set of numbers, terms, or expressions that are added together in a specific order.

## 2. How do you find the sum of a series?

To find the sum of a series, you need to add all the terms in the series together. The sum can be calculated using a formula or by adding the terms manually.

## 3. What is the formula for finding the sum of a series?

The formula for finding the sum of a series is S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term in the series.

## 4. What is the difference between an arithmetic and geometric series?

An arithmetic series is a series where each term is obtained by adding a constant number to the previous term, while a geometric series is a series where each term is obtained by multiplying the previous term by a constant number.

## 5. How do you know if a series is convergent or divergent?

A series is convergent if the sum of its terms approaches a finite number as the number of terms increases, and divergent if the sum approaches infinity or does not have a definite value. The convergence or divergence of a series can be determined by applying mathematical tests such as the ratio test or the integral test.

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