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  • HINT $\ $ Put $\rm\ \ x = 1+a\ \ $ in $\rm\displaystyle\ \ \frac{x^n -1}{x-1}\ =\ x^{n-1}+\:\cdots\: +x+1\ \ge\ n\ $ for $\rm\ x\ge 1$ Many induction problems are best solved in this manner, i.e. by transforming them into a form that makes the induction completely trivial.
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