Help Needed: Solving a Proof in Algebra

In summary, the conversation is about a problem and attempted solution involving induction and proofs. The problem is to determine what 2*(2^n) is equal to and the solution involves using the formula (2^n-1)+2^{(n+1)-1}=2^{n+1}-1. However, there is confusion about how to apply the formula correctly, leading to an incorrect solution. The issue is resolved with the realization that 2*2^n is equal to 2^(n+1) and not 2^2n.
  • #1
EsponV
15
0
Greetings,

It's been awhile since I've done induction or proofs in general, but I could not figure out where I went wrong on this one for the life of me. If anyone has an idea it would be much appreciated. I've uploaded a picture of the problem in the book as well as of my work. I thought I did everything correct but the algebra isn't working out.

Thanks all.

Problem (12): http://imageshack.us/m/30/7931/20110512190557593.jpg

Attempted Solution: http://imageshack.us/m/812/3723/2011051222200544.jpg
 
Last edited:
Physics news on Phys.org
  • #2
What is 2*(2^n) equal to? [Hint: not 2^(2n)]
 
  • #3
Right, so isn't 2*(2^n) = 2^(n+1) ?

But then I end up with 2^(2n) = 2^(n+1) which eventually leads to n = 1, yes?
 
  • #4
EsponV said:
Right, so isn't 2*(2^n) = 2^(n+1) ?

But then I end up with 2^(2n) = 2^(n+1) which eventually leads to n = 1, yes?

I don't understand how you could end up with [tex]2^{2n}=2^{n+1}[/tex] again. If you apply the correct formula in the line

[tex](2^n-1)+2^{(n+1)-1}=2^{n+1}-1[/tex]

then surely you'd end up with something else??
 
  • #5
Ah, I had been incorrectly stating that 2^n + 2^n = 2^2n instead of 2*2^n = 2^n+1. Thanks for the help, sorry about the algebra error.
 

1. What is a proof in algebra?

A proof in algebra is a logical argument that demonstrates the validity of a mathematical statement. It is used to show that a certain equation or expression is true for all values of the variables involved.

2. How do I approach solving a proof in algebra?

When solving a proof in algebra, it is important to carefully read and understand the statement or problem. Then, you can use known algebraic rules and principles to manipulate the given equations or expressions until you reach a conclusion that proves the statement to be true.

3. What are some common strategies for solving a proof in algebra?

Some common strategies for solving a proof in algebra include using the properties of equality, substitution, and direct or indirect proof. It is also helpful to break down the problem into smaller steps and work backwards from the desired conclusion.

4. What are some tips for avoiding mistakes when solving a proof in algebra?

To avoid mistakes when solving a proof in algebra, it is important to double check all your steps and calculations. It can also be helpful to use different colors or symbols to keep track of your work and to look for patterns or relationships between the given equations or expressions.

5. Can I use a calculator when solving a proof in algebra?

It depends on the specific problem and the rules set by your teacher or professor. In some cases, a calculator may be allowed to help with complex calculations, but it is important to show all your work and reasoning in order to receive full credit.

Similar threads

  • Calculus and Beyond Homework Help
Replies
6
Views
983
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
852
  • Calculus and Beyond Homework Help
Replies
24
Views
4K
  • Science and Math Textbooks
Replies
11
Views
2K
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
3K
Replies
4
Views
925
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
Back
Top