1. Geometric Series Recall that a geometric sequence is a sequence in which the ratio between successive terms is a constant. For example, the sequence g=1, 2, 4, 8, 16, 32, 64, … Has constant ratio 2. A geometric series is the sum of the terms of a geometric sequence, i.e.: S=1+2+4+8+16=31. As with arithmetic series, geometric series can be finite or infinite.

2. Geometric Series To find a general formula for the sum of a geometric series, we will use a technique similar (but not identical) to that used for arithmetic series… We will start with the first four terms of the series with g 1 =1 and r =2. To get the second equation, what did we multiply by? Now, we can subtract the equations:

3. Geometric Series Ok, now the general formula for the nth partial sum of a geometric sequence:

4. Try these: 1. 2.In a set of ten Russian nesting dolls, each doll is 5/6ths the height of the taller one. If the height of the first doll is 15cm, what is the total height of the dolls?

5. Suppose you have two children who marry (not to each other) and each of them has two children. Each of these offspring has two children, and so on. If all of the progeny marry, but none marry each other, and all have two children, in how many generations will you have 1000 descendants? Count your children as Generation 1.