Calculus Unit 13

Big Idea:

Series

Student Expectations:

Focus Standards

EU 4.1: The sum of an infinite number of real numbers may converge.

• EK 4.1A1: The partial sum is defined as the sum of the first terms of a sequence.
• EK 4.1A2: An infinite series of numbers converges to a real number (or has a sum ) if and only if the limit of its sequence of its partial sums exists and equals .
• EK 4.1A3: Common series of numbers include geometric series, the harmonic series, and series.
• EK 4.1A4: A series may be absolutely convergent, conditionally convergent, or divergent.
• EK 4.1A5: If a series converges absolutely, it converges.
• EK 4.1A6: In addition to examining the limit of the sequence of partial sums of the series, methods for determining whether a series of numbers converges or diverges are the term test, the comparison test, the limit comparison test, the integral test, the ration test, and the alternating series test.
• EK 4.1B1: If is a real number and is a real number such that , then the geometric series
• EK 4.1B2: If an alternating series converges by the alternating series test, then the alternating series error bound can be used to estimate how close a partial sum is to the value of the infinite series.
• EK 4.1B3: If a series converges absolutely, then any series obtained form it by regrouping or rearranging the terms has the same value.

Student Learning Targets:

• I will determine whether a series converges or diverges
• I will determine or estimate the sum of a series

Essential Questions:

Extra Information:

Adopted Textbook:

District Grading Policy

Texas Gateway Online Resource Center