1. ## Mathematical proof help

Proofs seem to be my weakest point when it comes to math. My teacher says that it is like an art form...one that will take me a very long time to understand.

Here is my question:

Prove the following by induction, where n is a positive integer.

1+2+3+4+....+ 2^(2-1) = 2^n - 1

My knowledge of proofs is very basic. I can only do things like "prove root3 is irrational" etc. I have trouble with them becasue there is no solid set of formulas you can use.

2. are you sure it is:

1+2+3+4+...+2^(2-1)?

THis would be 1+2+3+4+...+2

3. Originally Posted by jzellt
are you sure it is:

1+2+3+4+...+2^(2-1)?

THis would be 1+2+3+4+...+2
My mistake. It is 2^(n-1).

4. Originally Posted by RAz
Proofs seem to be my weakest point when it comes to math. My teacher says that it is like an art form...one that will take me a very long time to understand.

Here is my question:

Prove the following by induction, where n is a positive integer.

1+2+3+4+....+ 2^(2-1) = 2^n - 1

My knowledge of proofs is very basic. I can only do things like "prove root3 is irrational" etc. I have trouble with them becasue there is no solid set of formulas you can use.
Originally Posted by RAz
My mistake. It is 2^(n-1).
If that's the case, then surely the series is $1 + 2 + 4 + \cdots + 2^{n-1}$, NOT $1 + 2 {\color{red}+ 3} + 4 + \cdots + 2^{n-1}$.

Please take greater care with what you post.

Are you familiar with the three steps in proof by induction? Where do you get stuck in this process?

A hint for step 3: $(2^k - 1) + 2^k = 2 \cdot 2^k - 1 = 2^{k+1} - 1$.