Can I Represent ln(1+x) as a Power Series?

[donutmax]

hi!

are the following power series equivalent?

ln(1+x)=\sum_{n=0}^{\infty} \frac{(-1)^n n! x^{n+1}}{(n+1)!}
=\sum_{n=0}^{\infty} \frac{(-1)^n x^{n+1}}{n+1}

 

[The Chaz]

Yes.

 

[CRGreathouse]

\frac{(-1)^n n! x^{n+1}}{(n+1)!}=\frac{(-1)^n x^{n+1}}{(n+1)!/n!}=\frac{(-1)^n x^{n+1}}{(n+1)}

 

[The Chaz]

\frac{(-1)^n n! x^{n+1}}{(n+1)!}=\frac{(-1)^n x^{n+1}}{(n+1)!/n!}=\frac{(-1)^n x^{n+1}}{(n+1)}

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