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Math Help - 1/2 + 2/3 + 3/4 + 4/5+..............?

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    1/2 + 2/3 + 3/4 + 4/5+..............?

    1/2 + 2/3 + 3/4 + 4/5+.............?
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  2. #2
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    Re: 1/2 + 2/3 + 3/4 + 4/5+..............?

    Quote Originally Posted by AaPa View Post
    1/2 + 2/3 + 3/4 + 4/5+.............?
    What you have is \sum\limits_{k = 1}^\infty  {\frac{k}{{k + 1}}} and you know that \left( {\frac{n}{{n + 1}}} \right) \to 1 SO?
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    Re: 1/2 + 2/3 + 3/4 + 4/5+..............?

    It is divergent as any partial sum Sn of this series is greater than the coresponding sum of the Harmonic series Σ(1/n) which is divergent.
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    Re: 1/2 + 2/3 + 3/4 + 4/5+..............?

    One of the first things most people learn about infinite sums is:
    If \sum a_n converges then \lim_{n\to \infty} a_n= 0[/tex].

    Here, a_n= \dfrac{n-1}{n} which does NOT go to 0.
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