You never know when you might need math…. There is an end number.

9.5 SERIES

You never know when you might need math…

FINITE SERIESThere is an end number.

FINITE SERIESSUMMATION NOTATION

Number you go to

Index of summation (Number you start with)

EXAMPLES:

k1 k2 k3 k4 k5 k6

7

k4 k5 k6 k7

k2 k3 k4 k5

EXAMPLES:

EXAMPLES:k

FINITE ARITHMETIC

n=# of terms =1st term = last term

n=# of terms =1st termd=common difference

EXAMPLES:-7,-3,1,5,9,13

117, 110,103…33

=-7 =13n=6

117-3384/7=d 13 terms

FINITE GEOMETRIC

n=# of terms =1st term r= ratio

EXAMPLES:

=5r=3n=10

98415/3=32805

5,15,45…98415

INFINITE SERIESThere is no end.

INFINITE SERIESSUMMATION NOTATION

Goes to infinity (Never ends)

Index of summation (Number you start with)

GEOMETRIC

Converge=sumDiverge=no sum

Converge if |r|<1Not converge, sum=

EXAMPLES:

a r

6+3+3/2+3/4…Mult. By ½=r

4-2+1-1/2+1/4…r=-1/2

EXAMPLES:A ball is dropped at 5 feet. It rebounds to 80% of the last bounce. What is the total distance?

a=5r=.8

WORKS CITED Demana, Franklin, Bert K. Waits,

Gregory D. Foley, and Daniel Kennedy. Graphing Calculator Manual ; Precalculus, Graphical, Numerical, Algebraic :. Boston, MA: Pearson Addison Wesley, 2007. Print.

Krzykowski, Kylee. Notebook; Precalculus with Barber. Lincoln, H.S. 2013. Print.