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$\sum_{r=0}^n \frac{(-1)^{r-1}\binom{n}{r}(1-x)^r}{r}$

I tried it using $\binom{n}{r}$ = $\binom{n-1}{r}$+$\binom{n-1}{r-1}$ but I am not getting the desired result.

given answer is $\frac{1-x}{1}$+$\frac{1-x^2}{2}$ $\frac{1-x^3}{3}$+......+$\frac{1-x^n}{n}$

Baibhaw Kumar
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  • does the question begin from r=0 or 1? – NadiKeUssPar Mar 29 '23 at 05:27
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    Please see this article on MathSE protocol. As onerous as the article may appear to you, it provides a defense mechanism against the MathSE forum being used as a do my homework forum. In particular, please see the Edit-Tools section of the article, and the portion of the article that discusses showing work. It is irrelevant whether the problem is homework. What counts is whether the protocol is observed. – user2661923 Mar 29 '23 at 06:15

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