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

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    Series Sum
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
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thanksie037
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Homework Statement



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

Homework Equations





The Attempt at a Solution


i'm miserable at series. help?
 
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thanksie037 said:
Find the sum of the series s(x) = 1 +cos(x)+ (cos2x)/2!+(cos3x)/3!...

Homework Equations


Hi thanksie037! :smile:

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

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

What is a series?

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

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.

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.

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.

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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