The discussion revolves around proving the formula for the sum of a geometric series, specifically the expression 1 + 2 + 2^2 + 2^3 + ... + 2^(n-1) = 2^n - 1, using mathematical induction. Participants are exploring the steps necessary for a proof by induction.
The conversation is ongoing, with participants clarifying the requirements of the induction proof. Some guidance has been provided regarding the steps needed, but there is no consensus on the interpretation of "similar bases" or the overall approach to the proof.
Participants are reminded of the forum's rules against providing complete solutions, which influences the nature of the discussion. There is an emphasis on understanding the proof structure rather than solving the problem outright.
No, we won't "solve" it for you step by step. The Physics Forums rules expressly forbid this. Anyway, you're not "solving" this problem, you need to prove that the statement above is true for all integers n, n ≥ 1.Math325 said:Homework Statement
1 + 2 + 2^2 + 2^3 + ...+2^(n-1) = 2^n - 1
Homework Equations
Sum formula?
3. The Attempt at a Solution
I know you are suppose to use the base case and prove its true for k +1, but I'm not sure what to do for similar bases. Can someone please solve it step by step? Thanks!
This says that 1= 2^1- 1= 2- 1, 1+ 2= 2^2- 1= 4- 1= 3 , 1+ 2+ 4= 2^3- 1= 8- 1= 7, etc.Math325 said:Homework Statement
1 + 2 + 2^2 + 2^3 + ...+2^(n-1) = 2^n - 1
2. Homework Equations
Sum formula?
3. The Attempt at a Solution
I know you are suppose to use the base case and prove its true for k +1, but I'm not sure what to do for similar bases. Can someone please solve it step by step? Thanks!