Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Mathematics
Calculus
Geometric Series Convergence and Divergence
Reply to thread
Message
[QUOTE="Drakkith, post: 5448090, member: 272035"] I'm a little confused on geometric series. My book says that a geometric series is a series of the type: n=1 to ∞, ∑ar[SUP]n-1[/SUP] If r<1 the series converges to a/(1-r), otherwise the series diverges. So let's say we have a series: n=1 to ∞, ∑An, with An = 1/2[SUP]n[/SUP] An can be re-written as (1/2)[SUP]n[/SUP], which apparently makes it a geometric series with r=1/2. This converges to 1/(1-1/2) = 1/(1/2) = 2. However, I was under the assumption that I was supposed to factor out a 1/2 to make the series ∑1/2(1/2)[SUP]n-1[/SUP]. This would converge to (1/2)/(1-1/2) = (1/2)/(1/2) = 1. Why are these different? Which one is correct? [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
Calculus
Geometric Series Convergence and Divergence
Back
Top