What is the pattern in this summation expression?

In summary, simplifying as one expression means combining multiple terms or factors into a single, simplified expression, with no parentheses or like terms remaining. It is important because it can make a complex equation easier to understand and work with, while also eliminating potential errors. The steps for simplifying as one expression include combining like terms, using the distributive property, and eliminating parentheses by multiplying out terms. Some common mistakes include forgetting to combine like terms, incorrectly applying the distributive property, and making errors when multiplying out parentheses. Helpful tips for simplifying as one expression include double checking your work, using the order of operations, and being familiar with common algebraic rules.
  • #1
irony of truth
90
0
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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  • #2
Am I correct to say that you want to find the general term to express it as one summation?
 
  • #3
Yes. That is what I want to know... thank you for your clarification
 

What does it mean to "simplify as one expression"?

Simplifying as one expression means combining multiple terms or factors into a single, simplified expression, with no parentheses or like terms remaining.

Why is it important to simplify as one expression?

Simplifying as one expression can make a complex equation easier to understand and work with. It also helps to eliminate potential errors and makes it easier to solve the equation.

What are the steps for simplifying as one expression?

The steps for simplifying as one expression include combining like terms, using the distributive property, and eliminating parentheses by multiplying out terms.

What are some common mistakes when simplifying as one expression?

Some common mistakes when simplifying as one expression include forgetting to combine like terms, incorrectly applying the distributive property, and making errors when multiplying out parentheses.

Are there any shortcuts or tips for simplifying as one expression?

One helpful tip for simplifying as one expression is to always double check your work and make sure all terms have been properly combined and simplified. Additionally, using the order of operations and being familiar with common algebraic rules can make simplifying easier.

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