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Math Help - Determining whether series is convergent or divergent?

  1. #1
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    Determining whether series is convergent or divergent?

    Determine whether each series is convergent or divergent

    1. (1/2) -(3/8) + (9/32)

    2. 1+(3/1 x 2 x3)+ (5/1 x2 x 3 x 4 x 5)

    3. (4pi/3)+ 5pi/6 + pi/3


    The problem I am having on these is finding the general terms for the series so that I can use the comparison test. Any help would be appreciated as I have been trying to find the An term but these series throw me off.
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  2. #2
    Ted
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    Only three terms for each series?
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    Yes Im only given three terms.
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    I believe you were given the first three terms ... convergence/divergence is checked for infinite series.

    \frac{1}{2} - \frac{3}{8} + \frac{9}{32} - ... = \frac{3^0}{2^1} - \frac{3^1}{2^3} + \frac{3^2}{2^5} - ...

    this infinite series is \sum_{n=0}^{\infty} \frac{(-3)^n}{2^{2n+1}} = \frac{1}{2}\sum_{n=0}^{\infty} \left(\frac{-3}{4}\right)^n

    ... an infinite geometric series with common ratio between -1 and 1.

    what does that tell you?
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  5. #5
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    2. 1+(3/1 x 2 x3)+ (5/1 x2 x 3 x 4 x 5)
    1 + \frac{3}{3!} + \frac{5}{5!} + ... + \frac{2n+1}{(2n+1)!} + ... = \sum_{n=0}^{\infty} \frac{1}{(2n)!}

    converge? what test would you use?
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    3. (4pi/3)+ 5pi/6 + pi/3
    \frac{\pi}{6}\left(8+5+2+ ... \right)
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    I mean they are infinite series in that they keep going and have those .... at the end.
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