WARM UP. 12.4 Infinite Geometric Series EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will.

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Presentation transcript:

WARM UP

12.4 Infinite Geometric Series EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum.

EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Key Term Partial Sum – The sum S n of the first n terms of an infinite series. Partial Sum – The sum S n of the first n terms of an infinite series.

EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 1 Find partial sums

EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 1 Find partial sums

EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum.

EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 2 Find sums of infinite geometric series Find the sum of the infinite geometric series. a. 5(0.8) i – 1 8 i = b. + – –

EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 2 Find sums of infinite geometric series Find the sum of the infinite geometric series, if it exists d c. 8 n = 1 n –

EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 3 Standardized Test Practice

EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 4 Application Pendulums A pendulum that is released to swing freely travels 18 inches on the first swing. On each successive swing, the pendulum travels 80% of the distance of the previous swing. What is the total distance the pendulum swings?

EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 5 Write repeating decimals as fractions a. Write as a fraction in lowest terms.a. Write as a fraction in lowest terms.

EQ: When does an infinite geometric series have a sum and when does it not have a sum? Assessment: Students will write a summary explaining when a infinite geometric series has a sum. Example 5 Write repeating decimals as fractions Write the repeating decimal as a fraction in lowest terms. b

Homework Textbook Pg (3) and 37