SS- Geometric Series Lesson
Geometric Series
A poet wanted to share her poem with some friends to see what they thought. She sent her poem to three friends on Monday. On Tuesday, each of her friends sent the poem to three of their friends. On Wednesday, each recipient sends it to three other friends and this continues for 8 days. How many people read her poem after 8 days? Let's sketch this out and see...
In eight days, 9841 people, including herself had read her poem. As each day passes, the number of people who read her poem was three times the number the day before. Here is the list per day and the sum after eight days.
1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187 + 6561 = 9841
The numbers form a geometric sequence where a1=1 and r = 3. The sum of all the numbers is called a geometric series.
The video below uses an example to show you how the sum formula of a geometric finite series is derived.
The next two videos walks you through more examples of how to find the sum of the partial geometric series. Problem #3-8 are examples of finite geometric series. Problems #9-12 are infinite geometric series. Be sure to take notes!
What did you notice about problems #9-11? The common ratio for these problems were between -1 and 1, which results in an infinite series that has a sum. This is called a convergent infinite series.
What happened in problem #12 when the ratio was greater than 1? The infinite series did not have a sum! This is called a divergent infinite series.
Watch the video below to learn how to find the fraction for the repeating decimals. (Problems #13 - 15). Then learn how to solve real world problems involving geometric series.