Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Converging series

  1. Jan 17, 2016 #1
    Mod note: Moved from Homework section
    I know that ##1/n^4## converges because of comparison test with ##1/n^2## (larger series) converges .
    how do I know ##1/n^2## converges?
    coz I cannot compare it with ##1/n## harmonic series as it diverges.

    @REVIANNA, if you post in the Homework & Coursework sections, you must include an attempt. Your question seemed like more of a general question, but not a homework problem, so I moved your thread.
     
    Last edited by a moderator: Jan 17, 2016
  2. jcsd
  3. Jan 17, 2016 #2

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    Hint: for ##n\geq 2##: ##\frac{1}{n²}\leq \frac{1}{n²-n}=\frac{1}{n(n-1)}##
     
  4. Jan 17, 2016 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What is "coz"?

    Anyway, the slickest way to show that ##\sum 1/n^p ## converges if ##p > 1 ## and diverges if ##p = 1## (or ##p < 1##) is to note that for ##n \geq 2## we have
    [tex] \int_n^{n+1} \frac{dx}{x^p} < \frac{1}{n^p} < \int_{n-1}^n \frac{dx}{x^p} [/tex]
    so you can get easily-computed upper and lower bounds on ##\sum_{n=2}^N 1/n^p##.
     
    Last edited: Jan 17, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Converging series
  1. Convergent series (Replies: 5)

  2. Convergent Series (Replies: 4)

  3. Converge series (Replies: 3)

  4. Series convergence (Replies: 7)

  5. Series Converges. (Replies: 5)

Loading...