Math Is Fun Forum

Thank you for the explanation   I am aware my question is very vague, especially because English is not my mother tongue.

What I don't understand is the basis of this proof. For example, I have seen the proof by induction on geometric progression. Proof by induction use the basis that if it is true for n = 1 and we assume it is true for n = 1 to some number k and if we can show that it also work for k+1 then we can proof the validity of the geometric progression.

The proof by induction method use to proof geometric series can be applied to other progression as well by doing the same step:
1) proof n =1
2) assume correct for 1 to some number k
3) show it stands for k+1

of course they may be some progression that can't be proven this way, in that case we can just say proof by induction is not appropriate or not powerful enough to solve the problem.

I guess I can rephrase my question to: what is the general algorithm applied to the Geometric progression in order to get the proof as posted by Skul1?

Thank you for all the help