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9.5 SERIES
You never know when you might need math…
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FINITE SERIESThere is an end number.
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FINITE SERIESSUMMATION NOTATION
Number you go to
Index of summation (Number you start with)
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EXAMPLES:
k1 k2 k3 k4 k5 k6
7
k4 k5 k6 k7
k2 k3 k4 k5
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EXAMPLES:
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EXAMPLES:k
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FINITE ARITHMETIC
n=# of terms =1st term = last term
n=# of terms =1st termd=common difference
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EXAMPLES:-7,-3,1,5,9,13
117, 110,103…33
=-7 =13n=6
117-3384/7=d 13 terms
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FINITE GEOMETRIC
n=# of terms =1st term r= ratio
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EXAMPLES:
=5r=3n=10
98415/3=32805
5,15,45…98415
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INFINITE SERIESThere is no end.
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INFINITE SERIESSUMMATION NOTATION
Goes to infinity (Never ends)
Index of summation (Number you start with)
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GEOMETRIC
Converge=sumDiverge=no sum
Converge if |r|<1Not converge, sum=
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EXAMPLES:
a r
6+3+3/2+3/4…Mult. By ½=r
4-2+1-1/2+1/4…r=-1/2
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EXAMPLES:A ball is dropped at 5 feet. It rebounds to 80% of the last bounce. What is the total distance?
a=5r=.8
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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.