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Infinite Series - decreasing/increasing

  1. Apr 8, 2008 #1
    What exactly is the difference between "increasing/decreasing" and "strictly increasing/decreasing" ? is it similar to conditional and absolute convergence?
     
  2. jcsd
  3. Apr 8, 2008 #2
    [tex] (a_n)[/tex] is said to be increasing if for every [tex]n\in N[/tex] we have

    [tex] a_n_+_1\geq a_n[/tex], the same if [tex](a_n)[/tex] is decreasing then:

    [tex] a_n_+_1\leq a_n[/tex],

    If [tex](a_n)[/tex] is strictly increasing than [tex]\forall n\in N[/tex]

    [tex] a_n_+_1> a_n[/tex]. The same for decreasing.
     
  4. Apr 9, 2008 #3
    that v symbol means "for all n " correct?
     
  5. Apr 9, 2008 #4
    Yup, and along the same lines: [tex]\exists[/tex] means "there exists at least one".
     
  6. Apr 9, 2008 #5
    curved E ish symbol= all real numers?

    edit

    so what it means that "increasing" or "decreasing" has a point where a(n) is equal to a(n+1)? but strictly inc/dec means that no matter what value 'n' is, a(n) will always be > or < a(n+1)


    correct?
     
    Last edited: Apr 9, 2008
  7. Apr 9, 2008 #6
    Increasing means for all n [itex]a(n)\leq a(n+1)[/itex]. There might be some n's such that a(n)=a(n+1), but not necessarily.

    Strictly increasing means for all n a(n)<a(n+1), you can never have equality.
     
  8. Apr 9, 2008 #7
    thank you very much, i just needed clarification on that part of the equality
     
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