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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

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