MA19.FM.15

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

MA19.FM.15
Use mathematical induction to prove statements involving the positive integers.

Unpacked Content

Knowledge

Students know:

How to calculate combinations.

Skills

Students: Use recursive pattern to construct Pascal’s triangle.

Compare combinations to each row of Pascal's triangle to identify each row as the set of all combinations for a given set of objects.

Understanding

Students understand that:

Each row in Pascal’s triangle is the number of combinations of N take r where N is the row of the triangle starting with N=0 and r is the entry in the row from left to right.

Vocabulary

Pascal's Triangle
Recursion
Combinations

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.

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