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!

Series and Limits Problem

  1. Mar 29, 2016 #1
    1. The problem statement, all variables and given/known data
    I am supposed to determine whether the summation attached is convergent or divergent

    2. Relevant equations
    Alternating Series Test
    Test for Divergence

    3. The attempt at a solution
    The attempted solution is attached. Using the two different tests I am getting two different answers.

    Attached Files:

  2. jcsd
  3. Mar 29, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It is much preferred for you to type the problems rather than post a download.

    You have ##\frac 1 {\sqrt{n+1}}\to 0## which is correct. Now since$$
    0 \le \left | \frac {(-1)^n} {\sqrt{n+1}}\right | \le \frac 1 {\sqrt{n+1}}$$ how could the alternating one not go to zero? And, by the way, ##(-1)^\infty## makes no sense.
    Last edited: Mar 29, 2016
  4. Mar 29, 2016 #3
    Okay, you used the squeeze theorem which makes sense, but why doesn't the test for divergence work? Isn't (-1) undefined meaning the limit is undefined meaning the series is divergent?
  5. Mar 29, 2016 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, as I said, ##(-1)^\infty## makes no sense or, as you say, is undefined. What is happening in this problem is that the denominator is getting larger and the numerator is either plus or minus 1 for any n. The fraction gets small no matter the sign, so regardless of the alternating sign the fraction goes to zero.
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: Series and Limits Problem
  1. Limit of a series (Replies: 5)

  2. The limit of a series (Replies: 5)

  3. Limit of a Series (Replies: 4)

  4. Limit of series. (Replies: 6)

  5. Limit of series (Replies: 16)