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Math Help - easy series question

  1. #1
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    easy series question

    I just have some basic questions about series in calculus:

    is the Infinite Series always positive and getting smaller for it to converge?

    ----
    -----

    my other question is:

    is the telescoping series and collapsing series the same exact series?

    thanks.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    I just have some basic questions about series in calculus:

    is the Infinite Series always positive and getting smaller for it to converge?
    No.



    is the telescoping series and collapsing series the same exact series?

    thanks.
    Yes.
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  3. #3
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    Originally Posted by rcmango
    I just have some basic questions about series in calculus:

    is the Infinite Series always positive and getting smaller for it to converge?


    No.
    Okay, is an infinite series monotonic? Can an infinite series be bounded?

    thanks
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  4. #4
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    Quote Originally Posted by rcmango View Post
    Okay, is an infinite series monotonic? Can an infinite series be bounded?

    thanks
    Let s_n = 1

    Then,

    SUM (s_n) = +oo
    It is not bounded.

    And it does not need to be monotonmic.
    Let,
    t_n=(-1)^n
    Then,
    SUM (t_n) changes between -1 and +1 it cannot be monotomic.
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