GEOMETRIC SERIES
Feb 11th 2015
Geometric Series
nn tttttS ...4321
nSthn is called the partial sum
Equation
•First, call the whole sum "S": S=a + ar + ar2 + ... + ar(n-2)+ ar(n-1)
•Next, multiply S by r:Sr=ar + ar2 + ar3 + ... + ar(n-1) + arn
Now subtract the two equations
S − Sr = a − arn
Almost there
•Factor out S and a: S(1−r) = a(1−rn)
•Divide by (1-r): S = a(1−rn)/(1−r)
Finally we have the equation for a Geometric series
(For r not equal to 1)
We can rearrange to get another equation
Example: Find the sum of the finite geometric series:
3 – 6 + 12 – 24 + 48 – 96
Example:
Given 5 + 10 + 20 +…+ 1280 find its sum.
(can be done two ways)
Homework
Pg 53 #1-8