MA19.FM.14 | ALEX

Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.14

Use mathematical induction to prove statements involving the positive integers.

COS Examples
Examples: Prove that 3 divides $2^{2n}- 1$ for all positive integers n; prove that $1 + 2 + 3 + … + n = n(n + 1)/2$; prove that a given recursive sequence has a closed form expression.

Unpacked Content

Knowledge

Students know:

How to find equivalent expressions.

Skills

Students are able to:

Show that a statement is true for the first case, generally n=1.
Show that a statement is true for n=k+1 if it is assumed that the statement is true for n=k.

Understanding

Students understand that:

Proof by induction is a way of proving statements that includes two steps.

Vocabulary

Proof by mathematical induction

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