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

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SUMMARY

The sum of the series s(x) = 1 + cos(x) + (cos(2x))/2! + (cos(3x))/3! can be derived from the real part of the complex exponential series e^(ix). Specifically, the series converges to the expression Re(e^(ix)), which simplifies to cos(x). This conclusion is based on the properties of Taylor series expansions for 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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