Mathematical induction is a proof technique used to prove that a statement is true for all natural numbers. It involves proving a base case (usually when n=1) and then showing that if the statement is true for some n=k, it is also true for n=k+1. This allows us to extend the truth of the statement to all natural numbers.
To use mathematical induction to solve an equation, you first need to show that the statement (in this case, (n^3+5n)=6q) is true for the base case (usually when n=1). Then, you assume that the statement is true for some n=k and use this assumption to prove that it is also true for n=k+1. This process is repeated until you can conclude that the statement is true for all natural numbers.
The purpose of using mathematical induction is to prove that a statement is true for all natural numbers. This proof technique is particularly useful for proving statements about sequences, series, and recursive functions.
No, mathematical induction can only be used to prove statements that are true for all natural numbers. It cannot be used to prove statements about real numbers or complex numbers.
Mathematical induction is the appropriate proof technique to use when the statement you are trying to prove involves natural numbers and can be broken down into smaller cases. If the statement involves real numbers or complex numbers, other proof techniques such as direct proof or proof by contradiction may be more suitable.