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 $1\ge x>-1,$


Divide both sides by $x$ assuming $x\ne0$


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