Maclaurin Series: Find a_n for f(x) = 1/(1+3x)

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Homework Help Overview

The discussion revolves around finding the coefficients \( a_n \) for the Maclaurin series of the function \( f(x) = \frac{1}{1+3x} \). Participants are examining the derivatives of the function at zero to derive the series representation.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the derivatives of the function at zero and derives a formula for \( a_n \). Some participants question the presence of \( n! \) in the final expression and suggest rechecking the calculations. There is a hint provided to consider the notation for the nth derivative.

Discussion Status

The discussion is ongoing, with some participants expressing clarity after reviewing their work. There is an acknowledgment of a potential error regarding the factorial in the expression for \( a_n \), but no consensus has been reached on the correct formulation.

Contextual Notes

Participants are working under the constraints of homework guidelines, which may limit the extent of assistance provided. The notation for derivatives is also a point of confusion that remains unaddressed.

Kuno
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Homework Statement


find [tex]a_{n}[/tex] for [tex]f(x)\ =\ \frac{1}{1+3x}[/tex]

The Attempt at a Solution


I got:
f(0) = 1
f'(0) = -3
f''(0) = 9

The answer I ended up with was:
[tex]a_{n} \ = \ {(-1)}^n\frac{3^n}{n!}[/tex]

However, the answer in the back of my book has the same answer except it's not divided by n!.
 
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the n! is canceled out somehow. Recheck your workings.

Hint: Find f^n(x). I don't know what's the notation for the nth derivative of f(x)
 
Okay I see it now, thanks.
 
you're welcome :)
 

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