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Is this a convergent series?

  1. Jul 10, 2015 #1
    Mod note: Moved from a homework section.
    1. The problem statement, all variables and given/known data


    this is my lecturer's notes, he says it is a divergent series, but this seems like an obvious convergent series to me..
    could someone verify?

    2. Relevant equations

    https://www.dropbox.com/s/mc5rth0cgm94reg/incorrect maths.png?dl=0

    3. The attempt at a solution
     
    Last edited by a moderator: Jul 10, 2015
  2. jcsd
  3. Jul 10, 2015 #2

    SammyS

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    The series is the sum of all of the terms of the sequence. The sequence does converge to 2.

    What is the sum of an infinite number of terms each of which is at least a little greater than 2 ?
     
  4. Jul 10, 2015 #3
    Ah, I thought i was already looking at the series, but that was the terms of the sequence! thanks a lot :-)
     
  5. Jul 10, 2015 #4

    mathman

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  6. Jul 10, 2015 #5

    Mark44

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    Be sure you learn the difference between a sequence of terms, such as ##\{2 + e^{-m}\}_{m = 1}^{\infty}##, and a series, such as ##\sum_{m = 1}^{\infty}2 + e^{-m}##.
     
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