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Math Help - Calc 2 Sequence

  1. #1
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    Calc 2 Sequence

    Can anyone lend me a hand

    Write the first 5 terms of the sequence

    an = 3n!/(n-1)!

    Find the limit of the sequence if the limit exists

    an = (n-2)!/n!
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  2. #2
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    Quote Originally Posted by poopforbrains View Post
    Find the limit of the sequence if the limit exists

    an = (n-2)!/n!
    \frac{(n-2)!}{n!} = \frac{(n-2)!}{n(n-1)(n-2)!} = \frac{1}{n(n-1)}.
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  3. #3
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    Hello, poopforbrains!

    Write the first 5 terms of the sequence: . a_n \:= \:\frac{3n!}{(n-1)!}

    You're in Calculus 2 and you can't plug in values ??

    . . a_1 \: = \: \frac{3\cdot\!1!}{0!} \: = \: 3\cdot1 \: = \: 3

    . . a_2 \: = \: \frac{3\!\cdot\!2!}{1!} \: = \: 3\cdot2 \: = \: 6

    . . a_3 \: = \: \frac{3\!\cdot\!3!}{2!} \: = \: 3\cdot3 \: = \: 9

    . . a_4 \: = \: \frac{3\!\cdot\!4!}{3!} \: = \: 3\cdot4 \: = \: 12

    . . a_5 \: = \: \frac{3\!\cdot5!}{4!} \: = \: 3\cdot5 \: = \: 15



    Find the limit of the sequence if the limit exists
    . . a_n \:= \:\frac{(n-2)!}{n!}

    We have: . a_n \;=\;\frac{(n-2)!}{n(n-1)(n-2)!} \;=\;\frac{1}{n(n-1)}

    Hence: . \lim_{n\to\infty}\,\frac{1}{n(n-1)} \;=\;0

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