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tony700 said:Homework Statement
I work out the problem completely and it does not equal out. Having problems with two variable induction proofs (n and k) in this problem. Below is as far as I got, jpeg below
Homework Equations
The Attempt at a Solution
Are you absolutely required to use induction? If not, just writing out the product directly and simplifying is by far the easiest way to do the problem.tony700 said:Homework Statement
I work out the problem completely and it does not equal out. Having problems with two variable induction proofs (n and k) in this problem. Below is as far as I got, jpeg below
Homework Equations
The Attempt at a Solution
There could be several reasons why your induction proof is not working. One possibility is that your base case is incorrect, which means that your proof will not hold for the rest of the cases. Another possibility is that your induction hypothesis is incorrect or not strong enough to prove the desired equality. It is also possible that there is an error in your inductive step, where you incorrectly apply the induction hypothesis to prove the next case. It is important to carefully review your proof and identify where the error may be occurring.
If your induction proof is not working, one way to fix it is to carefully review your base case, induction hypothesis, and inductive step. Make sure that your base case is correct and that your induction hypothesis is strong enough to prove the desired equality. If necessary, you may need to modify your inductive step to properly apply the induction hypothesis. It may also be helpful to seek feedback from others or consult additional resources to help identify and fix any errors in your proof.
No, induction can only be used to prove equalities that follow a specific pattern. Induction works by proving a base case and then showing that if the equality holds for a particular case, it also holds for the next case. Therefore, the equality must have a clear and predictable pattern in order for induction to be successful. If the equality does not follow a pattern, then induction cannot be used to prove it.
No, there are other methods for proving equalities, such as direct proof, proof by contradiction, and proof by contrapositive. These methods may be more suitable for certain types of equalities or may be easier to use in certain situations. It is important to understand and be familiar with multiple proof techniques in order to choose the most appropriate method for a particular problem.
The best way to improve your skills in using induction for proofs is to practice. Start with simpler problems and work your way up to more complex ones. It may also be helpful to study sample proofs and understand the thought process behind them. Additionally, seeking feedback and guidance from others, such as teachers or peers, can also help improve your induction proof skills.