An infinite geometric sequence is geometric sequence that continues indefinitely. One is considered convergent if its terms approach a finite limit as the number of terms increases indefinitely.
For example, let's consider an infinite geometric sequence with $u_1 = 1$ and $r = \frac12$. The terms of this series go: $1, \frac12, \frac14, \frac18, \frac16...$. Eventually, as the terms go to infinity, each term gets closer and closer to 0, so we say it is convergent.
Condition for Convergence
Whether an infinite geometric sequence converges depends on the value of its common ratio.
The condition for convergence is:
$$|r|< 1$$
Unlock the rest of this chapter with aFreeaccount
Nice try, unfortunately this paywall isn't as easy to bypass as you think. Want to help devleop the site? Join the team at https://revisiondojo.com/join-us. exercitation voluptate cillum ullamco excepteur sint officia do tempor Lorem irure minim Lorem elit id voluptate reprehenderit voluptate laboris in nostrud qui non Lorem nostrud laborum culpa sit occaecat reprehenderit
Definition
Paywall
(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.
anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
Duis aute irure dolor in reprehenderit
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
Note
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.
Excepteur sint occaecat cupidatat non proident
Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia consequuntur magni dolores eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci velit.
Tip
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.
End of article
Flashcards
Remember key concepts with flashcards
11 flashcards
What is an infinite geometric sequence?
Lesson
Recap your knowledge with an interactive lesson
6 minute activity
Note
Infinite Geometric Sequences
An infinite geometric sequence is a geometric sequence that continues indefinitely without stopping.
The general form is: a,ar,ar2,ar3,…
Where a is the first term and r is the common ratio.
ExampleFor example, the sequence 2,1,21,41,81,… is infinite because it never ends.
DefinitionInfinite Geometric SequenceA sequence that continues indefinitely with a constant ratio between consecutive terms.
AnalogyThink of an infinite geometric sequence like a never-ending staircase where each step is a fixed fraction of the previous one.
