Power series representation of ln((1+2t)/(1-2t))

  • Thread starter kvkenyon
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  • #1
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Homework Statement


Find a power series representation for the function [tex]f(t) = \ln((1+2t)/(1-2t))[/tex]



Homework Equations



[tex]f(t) = \ln((1+2t)/(1-2t))[/tex]

The Attempt at a Solution



[tex]\ln(1+2t)-\ln(1-2t)[/tex]

take derivative of f(t) expanded

[tex]\frac{2}{1+2t}+\frac{2}{1-2t}[/tex]

[tex] 2 \int \frac {1}{1-(-2t)} + 2 \int \frac{1}{1-2t}[/tex]

[tex] 2 \int \displaystyle\sum_{n=o}^{\infty} -2^n x^n + 2 \int \displaystyle\sum_{n=0}^{\infty} 2^n x^n [/tex]

[tex] 2 \int 1 - 2x + 4x^2 - 8x^3 + 16x^4 +... + 2 \int 1 + 2x + 4x^2 + 8x^3 +16x^4 +32x^5+... [/tex]

then i combine them left with [tex] 2 \int 2 + 8x^2 + 32x^4 + .... [/tex]


then i get stuck
 
Last edited:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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I'm not sure why you switched from t to x. But then I'm not sure why you are stuck either. Just integrate term by term.
 
  • #3
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it was an accident im used to typing x and i didnt realize. also the answer choices that i have are with n-1 all over and i usually end up with n+1
 
  • #4
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well i got it...i ended up writing out cleaner when i posted it on here and then never realized the obvious...thanks
 

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