Power Series Representation of ln(1+7x)

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Homework Help Overview

The discussion revolves around finding a power series representation for the function f(x) = ln(1 + 7x). Participants explore different methods and connections related to power series and derivatives.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants discuss mechanical methods involving derivatives, while others suggest a quicker approach related to the function 7/(1 + 7x). Questions arise regarding the connection between ln(1 + 7x) and the suggested function.

Discussion Status

Participants are actively engaging with the problem, with some providing insights into the relationship between the derivative of ln(1 + 7x) and the function 7/(1 + 7x). There is a mix of understanding and uncertainty regarding the correctness of the results presented.

Contextual Notes

There is a mention of potential confusion regarding the connection between the functions and the validity of the derived series representation.

sportlover36
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how can i find a power series representation for a function like f(x)= ln(1+7x)?
 
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sportlover36 said:
how can i find a power series representation for a function like f(x)= ln(1+7x)?
There are at least two ways. One is very mechanical and involves taking the derivatives of your function. The other is probably a lot quicker. Can you find a power series for 7/(1 + 7x) = 1/(x + 1/7)? What's the connection between ln(1 + 7x) and 1/(x + 1/7)?
 
Im not really sure what the connection is but i got this at the answer...the sumation from n=1 to infinity -7x^n/n
 
The connection is that d/dx(ln(1 + 7x) = 7/(1 + 7x), or conversely, that ln(1 + 7x) = [itex]\int[/itex]7/(1 + 7x) dx.

If you didn't understand that connection, how did you get the result that you got? BTW, I'm not sure that your result is right.
 

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