# Regarding the power series, $1-{x\over 2}+{x^2\over 3}-{x^3\over4}+\dots$

I came across this power series while solving a problem.

$$1-{x\over 2}+{x^2\over 3}-{x^3\over4}+\dots$$

I calculated its radius of convergence and it turned out to be $$1$$.

Does this power series represent some well function in the given interval of convergence?

For $$1\ge x>-1,$$
$$\ln(1+x)=x-\dfrac{x^2}2+\dfrac{x^3}3-\dfrac{x^3}4+\cdots$$
Divide both sides by $$x$$ assuming $$x\ne0$$