# Power series of ln(1+x)

hi!

are the following power series equivalent?

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

## Answers and Replies

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