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

Question

anonymous · Answer

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

anonymous · Answer

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

anonymous · Answer

anonymous · Answer

anonymous · Answer