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something is wrong with that formula

what is wrong with the formula?

Looks correct to me.

Now you assume true up to some \(n\in\mathbb{Z}^+\). So \[(x^n-1)=(x-1)(x^{n-1}+x^{n-2}+...+x+1)\]

That make sense?

ok that makes a lot of sense. thank you so much!

You're welcome.

oh i read the exponent wrong, sorry