(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove by Induction that [tex]x^{k}-1=(x-1)(x^{k-1}+x^{k-2}+...+1)[/tex]

2. Relevant equations

None? I need to prove [tex]x^{k+1}-1=(x-1)(x^{k}+x^{k-1}+...+1)[/tex] by assuming this is true: [tex]x^{k}-1=(x-1)(x^{k-1}+x^{k-2}+...+1)[/tex]

3. The attempt at a solution

[tex]x^{k+1}-1=(x-1)(x^{k}+x^{k-1}+...+1)[/tex] - I tried substituting in the [tex]x^{k}[/tex] term, and expanding [tex]x*x^{k}-1[/tex], but it failed.

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# Induction Problem

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