## anonymous 5 years ago {n^2/2^n} does the sequence converge or diverge if it converges how do u find the limit?

1. anonymous
2. anonymous

Use the ratio test: $\lim_{n \rightarrow \infty} \frac{\frac{(n+1)^2}{2^{n+1}}}{\frac{2^n}{n^2}}$

3. anonymous

= $\lim_{n \rightarrow \infty} \frac{(n+1)^2}{2^{n+1}} \frac{2^n}{n^2} = \lim_{n \rightarrow \infty} \frac{1}{2}\frac{(n+1)^2}{n^2}$

4. anonymous

or you could watch the vid: http://www.youtube.com/watch?v=wV1FrqwZyKw&feature=feedlik

5. anonymous

which equals (1/2). So the ratio test says that if the ratio yeilds something less than 1, the series converges

6. anonymous

ohh ok i was trying to aproach this using the nth term test

7. anonymous
8. anonymous

if you try using the n-th term test, you'll get 0, which is inconclusive.

9. anonymous
10. anonymous
11. anonymous