1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Alternating series help

  1. Jan 22, 2008 #1
    1. The problem statement, all variables and given/known data

    Determine wheter the series is convergent or divergent. If it convergent, approximate the sum of the series correct to four decimal places.

    heres the equation: http://img251.imageshack.us/img251/2261/46755781zg9.png [Broken]

    2. Relevant equations

    3. The attempt at a solution

    This appears to be an alternating geometric series,

    Would it be okay to move the exponent k over everything? in other words: ( (-1)/k) )^k

    So then it looks alot like a geometric series, so then It converges by the rules of an alernating series, it is decreasing and it is approaching zero.

    So then to find its sum, i would do so by geometric series right?

    first term would be starting at k = 2, so: 1/2?

    then use 1/2 divided by 1 -r

    Am i on the right track? what is r??? is it also, 1/2?
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Jan 22, 2008 #2


    User Avatar
    Homework Helper

    Yes you can use k as the exponent of the whole because of the distributive property of exponentiation.
  4. Jan 22, 2008 #3
    how about the rest of what i'm doing here, this was my best hypothesis to approach the problem. I need help with the common ratio. i'm not sure what to use if its k^k ?
  5. Jan 22, 2008 #4


    User Avatar
    Homework Helper

    It isn't a geometric series because such series has a constant ratio between successive terms. However, that gives you a clue to the proof of its convergence. (Try a comparison test.) As for the estimate of the sum, do they want an analytical proof of some sort or just something carried out on a calculator (how many terms do you need to get to a precision of 10^-4 ?)
    Last edited by a moderator: May 3, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook