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

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The series s(x) = 1 + cos(x) + (cos 2x)/2! + (cos 3x)/3!... can be identified as the real part of the complex exponential series e^(ix). To find the sum, one can relate it to the Taylor series expansion of e^(ix), which includes both sine and cosine terms. The series converges and represents a function involving cosine. Understanding the relationship between real and complex series is crucial for solving this problem. The final sum can be expressed in terms of exponential functions.
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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:
 

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