1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sequence of 3/4^(2k). Show is convergent, find sum

  1. Jan 25, 2014 #1

    939

    User Avatar

    1. The problem statement, all variables and given/known data

    Consider the sequence ak = (3)/(4^(2k)). Show is convergent, find sum. Please check work.

    2. Relevant equations

    ak = 3/(4^2k)

    let s {n} be the series associated with the sequence. Cannot write summation notation here, but k starts at 1 (k = 1 on bottom) and infinity on top.

    3. The attempt at a solution

    ak1 = 0.1875
    ak2 = 0.01171875
    ak3 = 0.000732421876
    ak4 = 0.00004577636719

    ak4/ak3 = 0.0625

    Convergence: 1) r = 0.0625. r < 1, ∴ convergent
    Sum: 2) (0.1875)/(1-0.0625) = 0.2. Sum is 0.2
     
    Last edited: Jan 25, 2014
  2. jcsd
  3. Jan 25, 2014 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It is correct, if the summation starts with k=1.

    ehild
     
  4. Jan 25, 2014 #3

    939

    User Avatar

    Thanks! Yes, it does.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Sequence of 3/4^(2k). Show is convergent, find sum
  1. Sum of sequence (Replies: 8)

Loading...