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.SeattleScoute said:Homework Statement
Prove by incuction that for all positive intergers 1/(n(n+1)=(n/(n+1)
Homework Equations
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
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.
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.
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.
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.
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.