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**1. Homework Statement**

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

**2. Homework 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.