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

MA19.FM.15

Use mathematical induction to prove statements involving the positive integers.

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 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
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