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### Course: Algebra 2 (Eureka Math/EngageNY)>Unit 3

Lesson 12: Topic E: Lesson 29: Geometric series

# Geometric series intro

A geometric series is the sum of the terms of a geometric sequence. Learn more about it here. Created by Sal Khan.

## Want to join the conversation?

• At the end of the video Sal said we'll see if I can actually get a finite value, but how could you get a finite value if you are continuing to infinity?
• Here is a simple example:
∑ 3/10ⁿ over n=1 to ∞
With the first term you get 0.3
When you add the second term you get 0.33
With the third, you get 0.333
As you keep going toward infinity, you get closer and closer to ⅓. So, it is clear this infinite series has a sum of ⅓.
• I'm confused, is a geometric series (or sequence, because i'm still confused about that) a logarithm or exponential function?
• Sequence: an ordered list of things or terms (numbers). The list can be finite or infinite.
Series: the sum of the terms in an infinte sequence.
We use series to model functions, be they logarithmic functions, exponential functions, trigonometric functions, power functions etc.
• What does that Greek symbol mean?
• Sum, so in terms of series you would add everything up.
(1 vote)
• i cant understand
what is the difference between a sequence and series?
• A sequence is a collection of objects in a specific order. For example, because integers occur in a particular order, integers comprise a sequence. A sequence may have a finite number of members or it may have infinitely many members.

A series is the sum of all the members of a sequence.
• At Sal says that a (sub n) = 1(1/2)^(n-1). Why is the exponent (n-1)? Why can it not be (n)?
• The first index number of a sequence is n=1.
If we define a_n as 1(1/2)^(n), then the first term of the sequence in the video would be 1(1/2)^(1)= 1/2.
But the first term of the sequence in the video is given as 1.
If we define the sequence as Sal did, then we get 1(1/2)^(n-1) = 1(1/2)^(1-1) = 1(1/2)^0 = 1, as required.
• Someone might have already thought this, but are there no shapes involved in geometric sequences?
(1 vote)
• Sal, at , you wrote {a_n}_n=1.
What my question is, what is the meaning of n=1 there?
• This is a compact way of defining a sequence. It means that the sequence terms start from a_1 (indicated by the subscript) and go all the way to infinity (indicated by the superscript). The subscript and superscript following {a_n} are parts of a single definition that indicate lower and upper bounds of "n". So "n=1" that is below should necessarily be considered together with what is above (in this case, "infinity"). Just in case, "infinity" as an upper bound means that the sequence is infinite, i.e. goes on and on forever.
(1 vote)
• I am curious if there is any reason why its called a 'geometric series'?