For Regular Induction: Assume that the statement is true for n=k, for some integer k≥n0. For Strong Induction: Assume that the statement p(r) is true for all integers r, where \(n_0 ≤ ...For Regular Induction: Assume that the statement is true for n=k, for some integer k≥n0. For Strong Induction: Assume that the statement p(r) is true for all integers r, where n0≤r≤k for some k≥n0. If these steps are completed and the statement holds, we are saying that, by mathematical induction, we can conclude that the statement is true for all values of n≥n0.
Numbers can be organized into many different sequences. These sequences have patterns which can be used to predict the next number in the pattern. Misunderstandings may occur when we list few numbers ...Numbers can be organized into many different sequences. These sequences have patterns which can be used to predict the next number in the pattern. Misunderstandings may occur when we list few numbers in the sequence. Therefore it is wise to define sequences in terms of an explicit formula for the n ^th term.
