Mathematical induction problem solving question help

In summary, mathematical induction is a method of proof used to prove statements about natural numbers or other well-ordered sets. The approach involves proving a base case and then demonstrating that the statement holds for the next number. There are two types of induction, strong and weak, depending on the assumptions made. However, mathematical induction can only be used for well-ordered sets, not real numbers. Some tips for solving induction problems include looking for patterns and practicing different types of problems.
  • #1
hannahlawe
1
0
hi this question i just cannot do. i have no idea where to start:

a student is trying to recall the formula for the sum of cubes of consecutive numbers. she thinks it may be (n^3(n+1)^3) /8 or (n^2(n+1)^2)/4 . show by counter example one is incorrect and the other is correct by induction.

i can do the induction part its just the counter example i don't know where to start! thanks you
 
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  • #2
Try different n's, at some point (n=2) they give different results.
 

Related to Mathematical induction problem solving question help

1. What is mathematical induction?

Mathematical induction is a method of mathematical proof used to prove statements about natural numbers or other well-ordered sets. It involves proving a base case and then showing that if the statement holds for one number, it also holds for the next number.

2. How do I approach a mathematical induction problem?

First, identify the statement that needs to be proven. Then, prove the base case by plugging in the smallest possible value for the variable. Next, assume the statement holds for some arbitrary value and use it to prove that it also holds for the next value. Finally, conclude that the statement must hold for all values of the variable.

3. What is the difference between strong and weak induction?

In strong induction, the statement is assumed to hold for all numbers less than the current value of the variable. In weak induction, the statement is only assumed to hold for the previous value of the variable. Strong induction can be used when the statement depends on multiple previous values, while weak induction is typically used for simpler statements.

4. Can mathematical induction be used to prove all statements?

No, mathematical induction can only be used to prove statements about natural numbers or other well-ordered sets. It cannot be used to prove statements about real numbers or other non-well-ordered sets.

5. Are there any tips for solving mathematical induction problems?

One tip is to look for patterns in the statement and the values being used. It can also be helpful to work backwards from the desired conclusion to see what needs to be proven. Additionally, practicing with different types of induction problems can help develop a better understanding of the method.

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