Math 111 - 12/05/11

Test - Chapters 6 and 8 - Wed, Dec 7

Final - Sat, Dec 10, 1-3pm Clinton Hall 214

Study session Friday, December 9, 2011 in Jabara 127 from

8:30 am - 10:30 am.

Questions:

What's on the test?

6.1) Solve linear systems in 2 variables (two of these)

6.2) Solve linear systems in 3 variables (one of these)

6.7) Graph (systems of) linear inequalities (three of these - one as a system)

Chapter 8 problems probably 5 points each for balance

8.1) Find terms of a sequence (formula and recursive), Find the sum of a series in summation notation. (Three problems)

8.2) Arithmetic series and sequence (Three problems)

Learn Math Equation: a(_ n)_ = a(_ 1)_ + d(( n - 1))

Learn Math Equation: s(_ n)_ =(( a(_ 1)_ + a(_ n)_))s*(/ n,/ 2)/

8.3) Geometric series and sequence (Three problems)

Learn Math Equation: a(_ n)_ = a(_ 1)_s* r(^ n - 1)^

Learn Math Equation: s(_ n)_ =(/ a(_ 1)_(( 1 - r(^ n)^)),/ 1 - r)/

Learn Math Equation:(| r)| < 1 , s(_s8)_ =(/ a(_ 1)_,/ 1 - r)/

Ex: Find the sum of: Learn Math Equation: 1 6 - 8 + 4 - 2 + 1s.

it is geometric with Learn Math Equation: a(_ 1)_ = 1 6 , r = -(/ 1,/ 2)/

Learn Math Equation: s(_s8)_ =(/ 1 6,/ 1 -(( -(/ 1,/ 2)/)))/ =(/ 1 6,/(/ 3,/ 2)/)/ = 1 6s*(/ 2,/ 3)/ =(/ 3 2,/ 3)/

Ex: Find the sum of Learn Math Equation: 1 6 - 8 + 4 - 2 + 1 -(/ 1,/ 2)/ would use Learn Math Equation: s(_ n)_ =(/ a(_ 1)_(( 1 - r(^ n)^)),/ 1 - r)/ instead since it terminates.

Learn Math Equation:(s k = 5,s 2 3 7)s(/ 1,/ 2)/ k =(/ 5,/ 2)/ +(/ 6,/ 2)/ +(/ 7,/ 2)/ +(/ 8,/ 2)/ +s. +(/ 2 3 7,/ 2)/ arithmetic with Learn Math Equation: a(_ 1)_ =(/ 5,/ 2)/ , d =(/ 1,/ 2)/

Learn Math Equation: s(_ n)_ =(((/ 5,/ 2)/ +(/ 2 3 7,/ 2)/))s*(/ 2 3 3,/ 2)/ = ?

Learn Math Equation:(s k = 2,s 7)s k(^ 2)^ = 4 + 9 + 1 6 + 2 5 + 3 6 + 4 9 = ? just use calculator

For the final (not the test)

Exclamation mark - "Factorial notation"

5! means: Learn Math Equation: 5s* 4s* 3s* 2s* 1 = 1 2 0

8! = Learn Math Equation: 8s* 7s* 6s* 5s* 4s* 3s* 2s* 1 = 4 0 3 2 0

1! = 1

0! = 1