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.