Pg. 601 Homework Pg. 606#1 – 6, 8, 11 – 16 # … + (2n) 2 # (3n + 1) #5 #7(3n 2 + 7n)/2 #84n – n 2 #21#23 #26 #29 #33The series converges to ¼

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, …

11.3 Binomial Theorem Definitions A finite sum occurs in an expression like a + b, called a binomial since it has two terms, when it is raised to a power. Observations There are n + 1 terms in each Symmetry in coefficients and exponents Sum of exponents is n Begins and ends with first and last terms raised to the nth power

11.3 Binomial Theorem Pascal’s Triangle How is it created? What’s the next row? Comparisons How does this compare to what we just worked with? Expand:(a + b) 6 Expand:(2x + 3y 2 ) 4

11.3 Binomial Theorem Binomial Coefficients Pascal’s Triangle works for relatively small values, but what if you want to expand something much larger? We use a factorial to do so! n! = … n 3! = 8! = If n and r are two nonnegative integers, the number called the binomial coefficient n choose r is defined by: