Pg. 395/589 Homework Pg. 601#1, 3, 5, 7, 8, 21, 23, 26, 29, 33 #43x = 1#60see old notes #11, -1, 1, -1, …, -1#21, 3, 5, 7, …, 19 #32, 3/2, 4/3, 5/4, …, 11/10#4-2, 4, -6, 8, …, 20 #50, 7/3, 13/2, 63/5, …, 999/11 #64/3, 1, 4/5, 2/3, …, 1/3 #7-2, 3/2, -4/3, 5/4, …, 11/10 #83/8, 9/8, 27/8, 81/8, …, 59,049/8 #17diff = 4 a n = 2 + 4n a 10 = 42 #18diff = 5 a n = n a 10 = 41 #21ratio = 3 a n = 2(3) n – 1 a 8 = 4374 #22ratio = -2 a n = 1(-2) n – 1 a 8 = -128

11.2 Finite and Infinite Series Series A series {S n } is a sum of the terms of a sequence {a n }. S 1 = a 1 S 2 = a 1 + a 2 S 3 = a 1 + a 2 + a 3 S 4 = a 1 + a 2 + a 3 + a 4 S 5 = a 1 + a 2 + a 3 + a 4 + a 5 Sigma Notation If you want to find S n that can be done by writing the term in sigma notation. “The Big E” means add everything up! It is the sigma notation. The sum it equals is the expanded notation.

11.2 Finite and Infinite Series Example: Expand the following sum: Summation Properties Let {a n } and {b n } be two sequences and n be a positive integer. Then:

11.2 Finite and Infinite Series Example: Combine the following expression into a single sum: Summation Formulas The following are true for all positive integers n.

11.2 Finite and Infinite Series Example: Simplify: Convergence vs. Divergence Convergence: Divergence:

11.2 Finite and Infinite Series Sigma Notation Write the following sequences in Sigma Notation: … + 29 – – – 2 + … Use Sigma Notation to write the nth partial sum of the sequence: -8, -6, -4, … -3, -6, -9, -12, …