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Math Help - series limit

  1. #1
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    series limit

    a_{n} = \frac{1}{n+1} + \frac{1}{n+2} + ... \frac{1}{2n}

    what is the limit ?
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  2. #2
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    Hii

    Im trying to learn the same things so make sure to check my answer with someone else here but what I noticed is that the difference between each term is 1. Doesn´t that imply that this is an aritmetic series?
    There is a formula for that and that is \sum{a_1}+{a_2}....+a_n = \frac{n(a_1+a_n)}{2}
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  3. #3
    Super Member girdav's Avatar
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    We have a_{n+1}-a_n = \frac 1{2n+1}+\frac 1{2n+2}-\frac 1{n+1} <br />
= \frac 1 {\left(2n+1\right)\left(2n+2\right)} so you can write
    a_n as a sum.
    Then you will have to study the convergence of a serie.
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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