- #1
kevin3295
- 5
- 1
Homework Statement
ln(1-X), |x|<1
Homework Equations
Could someone verify if it was developed correctly?
The Attempt at a Solution
[tex]
ln(1-x) = \sum_{n=0}^\infty \left (a_nx^n\right )
[/tex]
[tex]
1+a+a^2+a^3+a^4+a^5+a^6... = 1/(1-a)
[/tex]
[tex]
a=x
[/tex]
[tex]
1+x+x^2+x^3+x^4+x^5+x^6... = 1/(1-x)
[/tex]
[tex]
∫1+x+x^2+x^3+x^4+x^5+x^6...dx = ∫1/(1-x) dx
[/tex]
[tex]
x+(x^2)/2+(x^3)/3+(x^4)/4+(x^5)/5+(x^6)/6... = - ln(x-1)
[/tex]
[tex]
ln(1-x) = - \sum_{n=1}^\infty \left (x^n / n \right )
[/tex]
Thanks for your time
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