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: Determine if the sum Converges or Diverges

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data


    3. The attempt at a solution

    1. I have no idea. I know that the summation of the series converges.

    2. I think it would diverge because the limit of the function does not equal zero.

    3. I have tried the ratio test and got 1. Can't use the alternating series test because when ignoring signs the function increases.
  2. jcsd
  3. Dec 4, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    For 3 what's the limit of (5n-1)/(n+5) and what does that tell you about convergence? For 1 I think they might be asking you to estimate the difference using an integral.
  4. Dec 4, 2011 #3


    User Avatar
    Homework Helper

    2) is correct
    3) Think about the function [itex]f(x)=\ln x[/itex]
    Last edited: Dec 4, 2011
  5. Dec 4, 2011 #4
    The limit of (5n-1)/(n+5) as x approaches infinity equals 5 thus meaning that the series in divergent? I think
  6. Dec 4, 2011 #5

    I'm not sure what [itex]f(x)=\ln x[/quote] means. Can you plus explain.
  7. Dec 4, 2011 #6


    User Avatar
    Science Advisor
    Homework Helper

    Right. If the nth term of a series doesn't approach 0 then it's always divergent. Now can you write an integral that's greater than the difference in 1?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook