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Math Help - Determine whether the series converges, and if it converges, determine its value.

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    Determine whether the series converges, and if it converges, determine its value.

    Consider the series
    Determine whether the series converges, and if it converges, determine its value.

    I know it converges, I got 7/10, but it's wrong. Please help! =)
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    Quote Originally Posted by ewkimchi View Post
    Consider the series
    Determine whether the series converges, and if it converges, determine its value.

    I know it converges, I got 7/10, but it's wrong. Please help! =)
    \sum_{n =1}^{\infty}\frac{(-7)^{n- 1}}{10^n} = \frac{1}{10} - \frac{7}{100} + \frac{49}{1000} - \frac{343}{10\,000} + \dots - \dots.


    This is a geometric series with a = \frac{1}{10} and r = -\frac{7}{10}.

    Since |r| < 1, the series is convergent, and

    S_{\infty} = \frac{a}{1 - r}

     = \frac{\frac{1}{10}}{1 - \left(-\frac{7}{10}\right)}

     = \frac{\frac{1}{10}}{\frac{17}{10}}

     = \frac{1}{17}.
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