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]

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

He's everywhere I want to be!