anonymous
  • anonymous
{n^2/2^n} does the sequence converge or diverge if it converges how do u find the limit?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
http://www.youtube.com/watch?v=wV1FrqwZyKw&feature=feedlik
anonymous
  • anonymous
Use the ratio test: \[\lim_{n \rightarrow \infty} \frac{\frac{(n+1)^2}{2^{n+1}}}{\frac{2^n}{n^2}}\]
anonymous
  • anonymous
= \[\lim_{n \rightarrow \infty} \frac{(n+1)^2}{2^{n+1}} \frac{2^n}{n^2} = \lim_{n \rightarrow \infty} \frac{1}{2}\frac{(n+1)^2}{n^2}\]

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anonymous
  • anonymous
or you could watch the vid: http://www.youtube.com/watch?v=wV1FrqwZyKw&feature=feedlik
anonymous
  • anonymous
which equals (1/2). So the ratio test says that if the ratio yeilds something less than 1, the series converges
anonymous
  • anonymous
ohh ok i was trying to aproach this using the nth term test
anonymous
  • anonymous
http://www.youtube.com/watch?v=wV1FrqwZyKw&feature=feedlik
anonymous
  • anonymous
if you try using the n-th term test, you'll get 0, which is inconclusive.
anonymous
  • anonymous
http://www.youtube.com/watch?v=wV1FrqwZyKw&feature=feedlik
anonymous
  • anonymous
http://www.youtube.com/watch?v=wV1FrqwZyKw&feature=feedlik
anonymous
  • anonymous
http://www.youtube.com/watch?v=wV1FrqwZyKw&feature=feedlik

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