#### Math - 2018-19

# MA.13 - Finite and Infinite Convergent Series

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

*Adopted: 2016*

### BIG IDEAS

### 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.13_{1} **Use**
and **interpret** the notation: å, *n*, *n*th, and *a _{n}*.

·
MA.13_{3} Given the formula, **determine** the nth term, *a _{n}*,
for an arithmetic or geometric sequence.

·
MA.13_{4} Given the formula, **determine** the sum, *S _{n}*,
if it exists, of an arithmetic or geometric series.

·
MA.13_{2} **Derive**
the formulas associated with arithmetic and geometric sequences and series.

·
MA.13_{5} **Model**
and **solve** problems, using sequence
and series information.

·
MA.13_{6} **Distinguish**
between a convergent and divergent series.

·
MA.13_{7} **Discuss**
convergent series in relation to the concept of a limit.

### KEY VOCABULARY

*Updated: May 29, 2018*