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Math Help - alternating series test

  1. #1
    Junior Member
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    alternating series test

    Hi all,

    I was wondering for the following series:

    <br />
\sum_{n=1}^{\infty}\frac{(-1)^(n-1)(-1)^n}{n}<br />

    NOTE: in the numerator it is meant to be (-1)^(n-1) times by (-1)^n .... sorry i can't it get the code to work

    are you allowed to let a_n = (-1)^n/ n and say that since a_n is not >0 for all n>=1, therefore the series diverges?

    Thanks in advance,
    ArTiCk
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I was wondering for the following series:

    <br />
\sum_{n=1}^{\infty}\frac{(-1)^{n-1}(-1)^n}{n}<br />

    NOTE: in the numerator it is meant to be (-1)^(n-1) times by (-1)^n .... sorry i can't it get the code to work

    are you allowed to let a_n = (-1)^n/ n and say that since a_n is not >0 for all n>=1, therefore the series diverges?

    Thanks in advance,
    ArTiCk
    your a_n = \frac 1n here. so, \lim_{n \to \infty}a_n = 0

    Note that (-1)^{n - 1}(-1)^n = (-1)^{2n - 1} = -1, thus your series is \sum_{n = 1}^\infty \frac {-1}n, which is a divergent harmonic series. The alternating series test does not apply since you do not have an alternating series.
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