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Math Help - series limit and convergence

  1. #1
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    series limit and convergence

    am i correct ? not sure would like a little help please.

    got this sequence

    an =7-6n/3n+14

    i did this:

    an =-6n/3n + 1/2

    an = -12n/6n + 1

    an = 1/n + 2

    so for large numbers of n, 1/n converges to 0 and so converges to an = 2
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  2. #2
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    Quote Originally Posted by smartcar29 View Post
    am i correct ? not sure would like a little help please.

    got this sequence

    an =7-6n/3n+14

    i did this:

    an =-6n/3n + 1/2

    an = -12n/6n + 1

    an = 1/n + 2

    so for large numbers of n, 1/n converges to 0 and so converges to an = 2
    the nth term of the sequence converges to -2

    \lim_{n \to \infty} \frac{7-6n}{3n+14}

    \lim_{n \to \infty} \frac{\frac{7}{n} -6}{3+ \frac{14}{n}} = \frac{-6}{3} = -2<br />
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  3. #3
    Junior Member woof's Avatar
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    Quote Originally Posted by smartcar29 View Post
    i did this:

    an =-6n/3n + 1/2
    You can't break up the denominator because there is a sum there, so this is where your argument fails.
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