What is the pattern in this summation expression?

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The discussion focuses on identifying the pattern in the series expression x - (2/6)x^3 - (20/120)x^5 - (1080/5040)x^7 - (140400/362880)x^9. The user seeks to express the series as a summation from n = 1 to infinity in the form of (??) x^(2n + 1) / (2n + 1)!. The key challenge is to determine the general term for the coefficients 2, 20, 1080, and 140400, which are critical for forming a unified summation expression.

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irony of truth
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I need some help

I got an expression involving series...

x - (2/6)x^3 - (20/120)x^5 - (1080/5040)x^7 - (140400/362880)x^9 - ...

I remove x from my summation expression.. but

Right now, I can express as a summation from n = 1 to infinity of

(??) x^(2n + 1) / (2n + 1)!

That is.. what is my pattern in this: 2, 20, 1080, 140400,... ?
 
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Am I correct to say that you want to find the general term to express it as one summation?
 
Yes. That is what I want to know... thank you for your clarification
 

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