Anyone want to check my mathematical induction proof? its a long one

In summary, mathematical induction is a proof technique used to show that a statement is true for all natural numbers. It involves proving a base case and showing that if the statement is true for n, it is also true for n+1. Its purpose is to prove statements about sequences and series. The steps involved in a mathematical induction proof are proving the base case, assuming the statement is true for some arbitrary natural number, showing the inductive step, and concluding that the statement is true for all natural numbers. Common mistakes to avoid when using mathematical induction include forgetting to prove the base case and using incorrect logic or notation. A proof using mathematical induction is considered correct if it follows the proper steps and is logically sound, with a clear base case,
  • #1
mr_coffee
1,629
1
Directions: Evalute the sum, for n = 1, 2, 3, 4, and 5. Make a conjecture about a formula for this sume for general n, and prove your conjecture by mathematical induction.

StatusX helped me get the first part, so I know that is right, about making the conjecture.http://suprfile.com/src/1/3j13ycr/lastscan.jpg
http://suprfile.com/src/1/3j14smr/lastscan2.jpg Thanks I hope everyone can read it, i tried putting somthing behind the paper while scanning and still no luck.
 
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  • #2
looks ok to me... just clean up your expression in the last step
 
  • #3
thanks stunner!
 

1. How does mathematical induction work?

Mathematical induction is a proof technique used to show that a statement is true for all natural numbers (i.e. 1, 2, 3, ...). It involves proving a base case (usually when n = 1 or n = 0) and then showing that if the statement is true for n, it is also true for n+1.

2. What is the purpose of using mathematical induction in proofs?

The purpose of using mathematical induction is to prove that a statement is true for all natural numbers. It is a powerful and commonly used technique in mathematics and is especially helpful in proving statements about sequences and series.

3. Can you explain the steps involved in a mathematical induction proof?

The steps involved in a mathematical induction proof are as follows:

  1. Prove the base case (usually n = 1 or n = 0).
  2. Assume that the statement is true for some arbitrary natural number n.
  3. Show that if the statement is true for n, it is also true for n+1.
  4. Conclude that the statement must be true for all natural numbers.

4. What are common mistakes to avoid when using mathematical induction?

Common mistakes to avoid when using mathematical induction include:

  • Forgetting to prove the base case.
  • Assuming that the statement is true for n+1 without properly proving it.
  • Using incorrect or incomplete logic in the inductive step.
  • Using incorrect notation when writing the proof.

5. How do I know if a proof using mathematical induction is correct?

A proof using mathematical induction is considered correct if it follows the steps outlined in the previous questions and if each step is logically sound. It is also important to clearly state the base case, inductive hypothesis, and inductive step in the proof. Additionally, it is always a good idea to have someone else check your proof for errors or inconsistencies.

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