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

Second rule of comparison in math series

  1. Nov 4, 2004 #1
    I cant understand this [tex]\sum{A_n}\leq \sum{B_n}[/tex] having said this

    if [tex]\sum{B_n}[/tex] converges so does [tex]\sum{A_n}[/tex], okay that

    makes perfect sense but then the second rule of comparison is if [tex]\sum

    {A_n}[/tex] diverges then so does [tex]\sum{B_n}[/tex] diverges too...can

    anyone tell me how that makes sense? A proof maybe..?
  2. jcsd
  3. Nov 4, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    General result, if P implies Q, then not Q implies not P.

    replace P with sum Bn converges and Q sum An converges.
  4. Nov 5, 2004 #3


    User Avatar
    Staff Emeritus
    Science Advisor


    Given [tex]\sum{A_n}[/tex] does NOT converge.

    Now assume [tex]\sum{B_n}[/tex] DOES converge. Using the theorem you said "makes perfect sense", what does that tell you about [tex]\sum{A_n}[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?