Question

Determine whether the sequence converges or diverges. If it converges, nd the limit

n!/2^n

Answer 1

You can use the ratio test.
\[\lim_{n->\infty}\left|\frac{a_{n+1}}{a_n} \right|=\lim_{n->\infty}\frac{(n+1)!/2^{n+1}}{n!/2^{n}}=\lim_{n->\infty}\frac{(n+1)n!}{2 \times 2^n}\frac{2^n}{n!}\]\[=\lim_{n->\infty}\frac{n}{2} \rightarrow \infty\]

The sequence does not converge since the ratio in the limit is not less than 1.

Answer 2

nice!

Answer 3

Thanks ;)

Answer 4

\[\frac{n+1}{2}\]

Answer 5

A question.. So does it mean that you cant test some values as N... and see whats happening?

Answer 6

Can you rephrase that? I'm not sure what you mean.

Answer 7

n!/2^n... Put in some values, as a check.. ..n= 1, 2, 3

Answer 8

And see if it diverges or converges

Answer 9

I hope you didnt misunderstand me, it was just a question, if i would in some values, in the funktion , n!/2^n .. could i see right away if it diverges or converges..

Answer 10

Ah I see. No, because that's not actually testing for ALL n. The tests are derived from the definition of convergence.

Answer 11

You could get an idea, but it wouldn't prove it. That's all.

Answer 12

Okey, so u have to, show it for all n. like u did

Answer 13

Exactly.

Answer 14

Well, thx.

Answer 15

No worries.

Answer 16

Hehe, I thought this was XiaoHong's question.

Answer 17

So did i ;)

Answer 18

thanks

Answer 19

Welcome.