# Induction steps for two algebra problems

Hello,

Can you please assist with the induction step for this problem?

3. Prove that

1 + 2 + 2^2 + ... + 2^(n-1) = 2^n - 1

for every n > 1.

5. Prove that for any real number x and for all numbers n > 1,

x^n - 1 = (x - 1)(x^(n-1) + x^(n-2) + ... + x^(n-r) + ... + x + 1).

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#### Solution Summary

This solution reviews the method of mathematical induction through working out these two questions step-by-step. From this one-page pdf solution attached, one will have a clear view of the mathematical induction.

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