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

Prove that 1/(1-x) = 1 + x + x^{2}+ x^{3}+ ... + x^{n}/(1-x) for n>=2

2. Relevant equations

3. The attempt at a solution

I'm not really all that sure how to begin. The base case would be 1/(1-x) = x^{2}/(1-x) and the induction hypothesis would be 1/(1-x) = 1 + x + x^{2}+ x^{3}+ ... + x^{n}/(1-x) but I don't know what the n+1 case is and how to prove that it holds. I guess the n+1 case would logically be 1/(1-x) = 1 + x + x^{2}+ x^{3}+ ... + x^{n}/(1-x) + x^{n+1}/(x-1), but I don't know how to show algebraically that the left hand side equals the right hand side.

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# Proof by Induction

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