Unit 5 – Series, Sequences and Limits Section 5

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Unit 5 – Series, Sequences and Limits Section 5 Unit 5 – Series, Sequences and Limits Section 5.5 – Infinite Series and Sigma Notation Calculator Required

1, 4, 7, 10, 13, …. Infinite Arithmetic No Sum 3, 7, 11, …, 51 Finite Arithmetic 1, 2, 4, …, 64 Finite Geometric 1, 2, 4, 8, … Infinite Geometric r > 1 r < -1 No Sum Infinite Geometric -1 < r < 1

Find the sum, if possible:

Find the sum, if possible:

Find the sum, if possible:

Find the sum, if possible:

Find the sum, if possible:

The Bouncing Ball Problem – Version A A ball is dropped from a height of 50 feet. It rebounds 4/5 of it’s height, and continues this pattern until it stops. How far does the ball travel? 50 40 40 32 32 128/5 128/5

The Bouncing Ball Problem – Version B A ball is thrown 100 feet into the air. It rebounds 3/4 of it’s height, and continues this pattern until it stops. How far does the ball travel? 100 100 75 75 225/4 225/4

UPPER BOUND (NUMBER) SIGMA (SUM OF TERMS) NTH TERM (SEQUENCE) LOWER BOUND (NUMBER)

Rewrite using sigma notation: 3 + 6 + 9 + 12 Arithmetic, d= 3

Rewrite using sigma notation: 16 + 8 + 4 + 2 + 1 Geometric, r = ½

Rewrite using sigma notation: 19 + 18 + 16 + 12 + 4 Not Arithmetic, Not Geometric 19 + 18 + 16 + 12 + 4 -1 -2 -4 -8

Rewrite the following using sigma notation: Numerator is geometric, r = 3 Denominator is arithmetic d= 5 NUMERATOR: DENOMINATOR: SIGMA NOTATION: