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## Homework Statement

I am trying to show that [tex]\sum{ \frac{x^n}{n}} = -ln(1-x)[/tex]

But I am doing something wrong and I cant find my mistake.

Please find my mistake and let me know what it is.

Thanks

## The Attempt at a Solution

set [tex] f(x)=\sum {\frac{x^n}{n}} [/tex]

then [tex] f'(x)= \sum {x^n-1} [/tex]

so [tex] xf'(x)=\sum{x^n} = \frac {1}{1-x} [/tex]

which means that [tex] f'(x)=\frac {1}{x} - \frac{1}{1-x} [/tex]

integrtang we get [tex] f(x)=ln|x|-ln|1-x| [/tex]

which is bad