I want to show that [tex] \sum_{k=0}^{n} x^{k} = \frac{1-x^{n+1}}{1-x} [/tex] using the additive, homogeneous, and telescoping properties of summation. In a hint it says to write the sum as [tex] (1-x)\sum_{k=0}^{n} x^{k} [/tex]. How did they arrive at this? Did they factor out the [tex] 1-x [/tex]. I dont see how they did this. I would then write [tex] x^{k} [/tex] as [tex] x^{k+1} - (x-1)^{k+1} [/tex]. Then what?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks

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# Homework Help: Showing a Sum

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