Suppose that $x\ne 1$ and $n\in\mathbb{N}^*$. Prove with induction that $$\sum_{k=0}^{n-1}x^{k}=\frac{x^n-1}{x-1}$$
It seems simple but I have tried for I don't know how long by now... Anyone can manage this?
2026-05-16 17:07:25.1778951245
Prove with induction that $\sum_{k=0}^{n-1}x^{k}=\frac{x^n-1}{x-1}$
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