# MA.13 - Finite and Infinite Convergent Series

MA.13  the student will determine the sum of finite and infinite convergent series.

### UNDERSTANDING THE STANDARD

·  Examination of infinite sequences and series may lead to a limiting process.

·  Arithmetic sequences have a common difference between any two consecutive terms.

·  Geometric sequences have a common ratio between any two consecutive terms.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  MA.131  Use and interpret the notation: å, n, nth, and an.

·  MA.133  Given the formula, determine the nth term, an, for an arithmetic or geometric sequence.

·  MA.134  Given the formula, determine the sum, Sn, if it exists, of an arithmetic or geometric series.

·  MA.132  Derive the formulas associated with arithmetic and geometric sequences and series.

·  MA.135  Model and solve problems, using sequence and series information.

·  MA.136  Distinguish between a convergent and divergent series.

·  MA.137  Discuss convergent series in relation to the concept of a limit.

### KEY VOCABULARY

Updated: May 29, 2018