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Math Help - Sequences question

  1. #1
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    Sequences question

    Hi

    Show that the sequence given by

    an = 1/(n+1) + (1/(n+2)) + (1/(n+3)) +...... (1/(n+n')) converges.
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  2. #2
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    Quote Originally Posted by champrock View Post
    an = 1/(n+1) + (1/(n+2)) + (1/(n+3)) +...... (1/(n+n')) converges.
    Have you noticed that a_n  = \sum\limits_{k = 1}^n {\frac{{\frac{1}{n}}}{{1 + \frac{k}{n}}}} ?

    That is an approximating sum for \int_0^1 {\frac{{dx}}{{1 + x}}} .
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  3. #3
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    i am slightly confused. cant this sequence be considered as an extension of the 1 + 1/1 + 1/2 + 1/3 sequence?

    So the sequence goes like 1 + 1/1 + 1/2 + 1/3 ..... 1/(n+1) + (1/(n+2)) + (1/(n+3)) +...... (1/(n+n')) ...... 1/(n+n'+1) .... and so on ?
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