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

New 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