Mississippi Math A3.N.3

MathGrades 9–12Number and Quantity (N) Explore and Illustrate the Characteristics and Operations Connecting Sequences and Series

The Standard

Calculate limits based on convergent and divergent series.

2025 Mississippi College- and Career-Readiness Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students find the partial sums of a series and decide whether they approach a finite number. For a geometric series, they use the first term and common ratio to calculate that limit when one exists.
What Mastery Looks Like: Given 3 + 1.5 + 0.75 + ..., a student finds a limit of 6. Given 1 - 1 + 1 - 1 + ..., they show that the partial sums alternate between 1 and 0, so no limit exists.
Common Misconceptions: Some students think terms shrinking to zero guarantee a finite sum, but 1 + 1/2 + 1/3 + ... keeps growing. Others use the infinite geometric sum formula when the common ratio is 1 or -1.
How to Assess It: Exit ticket: Find the limit of the partial sums for 4 + 2 + 1 + ... and 2 - 2 + 2 - 2 + .... Show the first four partial sums for each and explain your answers.

Lesson moves

Cut paper strips 1, 1/2, 1/4, and 1/8 unit long; lay them end to end and predict the total length after infinitely many strips.
Ask students to explain why 1 + 1/2 + 1/4 + ... approaches 2 while 1 + 2 + 4 + ... does not.
Give pairs three series cards: 3 + 1.5 + 0.75 + ..., 2 + 2 + 2 + ..., and 5 - 5 + 5 - .... Have them sort by whether the partial sums have a finite limit.
A ball drops 1 meter and bounces to half its previous height each time; have students calculate its total travel distance.

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