# Another Matematical Induction Problem

• SeattleScoute
In summary, the conversation is about trying to prove, using induction, that the equation 1/(n(n+1)) = (n/(n+1)) holds for all positive integers. The attempt at a solution involves proving it for n=1 and then finding a way to set the equation for n+1, but a counterexample has been given that suggests the equation may not be generally true.
SeattleScoute

## Homework Statement

Prove by incuction that for all positive intergers 1/(n(n+1)=(n/(n+1)

## The Attempt at a Solution

I have proved this is true for n=1. I need to find a way to set the equation for n+1

Welcome to physicsforums(=

does it holds for all positive integer?
can you check for some case like positive integer 5 .

$$\frac{1}{5(5+1)}\neq\frac{5}{5+1}$$

SeattleScoute said:

## Homework Statement

Prove by incuction that for all positive intergers 1/(n(n+1)=(n/(n+1)

## The Attempt at a Solution

I have proved this is true for n=1. I need to find a way to set the equation for n+1
Are you sure you have given us the problem exactly as stated. icystrike gave a counterexample to show that the equation above isn't generally true.

Note that you are missing two closing parentheses, that suggests something can be wrong with the equation.

## 1. What is mathematical induction?

Mathematical induction is a proof technique used to show that a statement is true for all natural numbers. It involves two steps: the base case, where the statement is shown to be true for the first natural number, and the inductive step, where it is shown that if the statement is true for some natural number, then it is also true for the next natural number.

## 2. How is mathematical induction used?

Mathematical induction is used to prove mathematical statements that involve the natural numbers, such as equations, inequalities, and divisibility statements. It is particularly useful for proving recursive formulas and properties of series and sequences.

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

The difference between weak and strong induction lies in the inductive step. In weak induction, we assume that the statement is true for a specific natural number, while in strong induction, we assume that the statement is true for all previous natural numbers. In other words, strong induction has a stronger inductive hypothesis and can be used to prove more complex statements.

## 4. Can mathematical induction be used to prove any statement?

No, mathematical induction can only be used to prove statements that involve the natural numbers. It cannot be used for statements that involve real numbers, such as inequalities or trigonometric identities.

## 5. Are there any limitations to using mathematical induction?

Yes, there are some limitations to using mathematical induction. It can only be used to prove statements about the natural numbers, and it may not be the most efficient or elegant proof technique for every statement. In some cases, other proof techniques such as direct proof or proof by contradiction may be more suitable.

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