SOLUTION: Prove by induction: 1+a+a^2+...+a^(n-1)=(a^n-1)/(a-1)

Question 962542: Prove by induction:
1+a+a^2+...+a^(n-1)=(a^n-1)/(a-1)

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!



Prove true for n=1: (There is only one term)





So it is true for n=1

Assume it is true for all n ≤ k



Add  to both sides



Simplifying the right side:









 

 





And that is exactly what you would get if you substitute
n=k+1 in .

So the formula is proved.

Edwin

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