13.04 Proof by induction
Interactive practice questions
By filling in the blanks, complete the statement that describes the process of mathematical induction.
The principle of mathematical induction states that a statement involving positive integers is true for all positive integers when two conditions have been satisfied:
The first condition states that the statement is true for the positive integer $\editable{}$
The second condition states that if the statement is true for some positive integer $k$k, it is also true for the next positive integer $\editable{}$
Read statements $A$A to $H$H below.
Select and list the statements, in the correct order, that explain how to use mathematical induction to prove a statement is true for every positive integer $n$n.
Is it possible to use mathematical induction to prove that statements are true for all real numbers $n$n?
Consider the statement:
$6+12+18+...+6n=3n\left(n+1\right)$6+12+18+...+6n=3n(n+1)